Кострикин, А. И (Алексей Иванович)
Overview
Works:  118 works in 457 publications in 5 languages and 4,792 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Editor, Other, Adapter, Honoree, Translator 
Classifications:  QA154.2, 512 
Publication Timeline
.
Most widely held works by
А. И Кострикин
Algebra I : basic notions of algebra by
I. R Shafarevich(
Book
)
31 editions published between 1986 and 2014 in 3 languages and held by 587 WorldCat member libraries worldwide
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights ..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 " ... which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 " ... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra ... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book  which reads as comfortably as an extended essay  breathes life into the skeleton and will be of interest to many classes of readers ..." The Mathematical Gazette, 1991 " ... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions  all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
31 editions published between 1986 and 2014 in 3 languages and held by 587 WorldCat member libraries worldwide
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights ..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 " ... which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 " ... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra ... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book  which reads as comfortably as an extended essay  breathes life into the skeleton and will be of interest to many classes of readers ..." The Mathematical Gazette, 1991 " ... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions  all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
Introduction to algebra by
A. I Kostrikin(
Book
)
53 editions published between 1977 and 2000 in 6 languages and held by 478 WorldCat member libraries worldwide
53 editions published between 1977 and 2000 in 6 languages and held by 478 WorldCat member libraries worldwide
Linear algebra and geometry by
A. I Kostrikin(
Book
)
25 editions published between 1988 and 2005 in English and held by 460 WorldCat member libraries worldwide
25 editions published between 1988 and 2005 in English and held by 460 WorldCat member libraries worldwide
Around Burnside by
A. I Kostrikin(
Book
)
19 editions published between 1990 and 2014 in English and held by 383 WorldCat member libraries worldwide
This is a truly encyclopaedic survey of the various aspects of the "restricted Burnside problem" and its surprising applications. Among many other things, it contains a detailed positive solution of the restricted Burnside problem for prime exponent, via Engel Lie algebras and socalled sandwiches. A new appendix to this translation contains a proof by E.I. Zel'manov of the existence of a recursive upper bound for the nilpotency class of a dgenerator finite group of prime exponent p. Informative and illustrative comments grace the end of each chapter, and there is an extensive bibliography
19 editions published between 1990 and 2014 in English and held by 383 WorldCat member libraries worldwide
This is a truly encyclopaedic survey of the various aspects of the "restricted Burnside problem" and its surprising applications. Among many other things, it contains a detailed positive solution of the restricted Burnside problem for prime exponent, via Engel Lie algebras and socalled sandwiches. A new appendix to this translation contains a proof by E.I. Zel'manov of the existence of a recursive upper bound for the nilpotency class of a dgenerator finite group of prime exponent p. Informative and illustrative comments grace the end of each chapter, and there is an extensive bibliography
Algebra II : noncommutative rings, identities by
A. I Kostrikin(
Book
)
19 editions published in 1991 in English and Undetermined and held by 377 WorldCat member libraries worldwide
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the bestknown example of a noncommutative alge 1 bra  Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of noncommutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry  for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the socalled microlocal analysis. The theory of operator algebras (Le
19 editions published in 1991 in English and Undetermined and held by 377 WorldCat member libraries worldwide
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the bestknown example of a noncommutative alge 1 bra  Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of noncommutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry  for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the socalled microlocal analysis. The theory of operator algebras (Le
Algebra VIII : representations of finitedimensional algebras by
Peter Gabriel(
Book
)
17 editions published between 1991 and 1992 in English and held by 326 WorldCat member libraries worldwide
17 editions published between 1991 and 1992 in English and held by 326 WorldCat member libraries worldwide
Algebra VI : combinatorial and asymptotic methods of algebra : nonassociative structures by
E. N Kuz'min(
Book
)
21 editions published between 1990 and 2011 in English and held by 315 WorldCat member libraries worldwide
21 editions published between 1990 and 2011 in English and held by 315 WorldCat member libraries worldwide
Algebra IX : finite groups of Lie type, finitedimensional division algebras(
Book
)
11 editions published in 1996 in English and held by 264 WorldCat member libraries worldwide
11 editions published in 1996 in English and held by 264 WorldCat member libraries worldwide
Proceedings of the International Conference on Algebra dedicated to the memory of A.I. Malcev by International Conference on Algebra(
Book
)
26 editions published in 1992 in English and held by 244 WorldCat member libraries worldwide
26 editions published in 1992 in English and held by 244 WorldCat member libraries worldwide
Second International Conference on Algebra : dedicated to the memory of A.I. Shirshov : proceedings of the second International
Conference on Algebra, August 2025, 1991, Barnaul, Russua by International Conference on Algebra(
Book
)
12 editions published in 1995 in English and held by 192 WorldCat member libraries worldwide
12 editions published in 1995 in English and held by 192 WorldCat member libraries worldwide
Algebra IV : infinite groups, linear groups : with 9 figures(
Book
)
1 edition published in 1993 in English and held by 184 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 184 WorldCat member libraries worldwide
Exercises in algebra : a collection of exercises in algebra, linear algebra, and geometry by
A. I Kostrikin(
Book
)
13 editions published between 1995 and 1996 in English and held by 150 WorldCat member libraries worldwide
13 editions published between 1995 and 1996 in English and held by 150 WorldCat member libraries worldwide
Algebra by
A. I Kostrikin(
Book
)
15 editions published in 1993 in English and held by 109 WorldCat member libraries worldwide
Group theory is one of the most fundamental branches of mathematics. This volume of the Encyclopaedia is devoted to two important subjects within group theory. The first part of the book is concerned with infinite groups. The authors deal with combinatorial group theory, free constructions through group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structure theory for Abelian, soluble and nilpotent groups. They have included the very latest developments; however, the material is accessible to readers familiar with the basic concepts of algebra. The second part treats the theory of linear groups. It is a genuinely encyclopaedic survey written for nonspecialists. The topics covered includethe classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to allmathematicians, physicists and other scientists including graduate students who use group theory in their work
15 editions published in 1993 in English and held by 109 WorldCat member libraries worldwide
Group theory is one of the most fundamental branches of mathematics. This volume of the Encyclopaedia is devoted to two important subjects within group theory. The first part of the book is concerned with infinite groups. The authors deal with combinatorial group theory, free constructions through group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structure theory for Abelian, soluble and nilpotent groups. They have included the very latest developments; however, the material is accessible to readers familiar with the basic concepts of algebra. The second part treats the theory of linear groups. It is a genuinely encyclopaedic survey written for nonspecialists. The topics covered includethe classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to allmathematicians, physicists and other scientists including graduate students who use group theory in their work
Combinatorial group theory and applications to geometry by
D. J Collins(
Book
)
3 editions published between 1991 and 1998 in English and held by 28 WorldCat member libraries worldwide
From the reviews of the first printing of this book, published as volume 58 of the Encyclopaedia of Mathematical Sciences: " ... This book will be very useful as a reference and guide to researchers and graduate students in algebra and and topology." Acta Scientiarum Mathematicarum, Ungarn, 1994 " ... The book under review consists of two monographs on geometric aspects of group theory: Combinatorial group theory and fundamental groups" by D.J. Collins and H. Zieschang ... : "Some problems of group theory related to geometry" by R.I. Grigorchuk and P.F. Kurchanov. ... Together, these two articles form a wideranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ... In summary, a very interesting book! Bulletin of the London Mathematical Society, 1996 " ... In both essays the authors give clear and comprehensive definitions, examples and statements (but not proofs) of theorems, so that the book can be understood by a reader with a minimal background in group theory or geometry. Such a reader, needing to find out what is known in this area, will find this a full and accessible store of information." Contemporary Physics, 1994 " ... This survey (Part II) presents for the first time that problems in monograph form and by the way offers a unifying treatment of the various approaches to their solutions, as far as they are known, together with hints to open problems. A titbit for every interested reader!" Monatshefte fr Mathematik, 1995
3 editions published between 1991 and 1998 in English and held by 28 WorldCat member libraries worldwide
From the reviews of the first printing of this book, published as volume 58 of the Encyclopaedia of Mathematical Sciences: " ... This book will be very useful as a reference and guide to researchers and graduate students in algebra and and topology." Acta Scientiarum Mathematicarum, Ungarn, 1994 " ... The book under review consists of two monographs on geometric aspects of group theory: Combinatorial group theory and fundamental groups" by D.J. Collins and H. Zieschang ... : "Some problems of group theory related to geometry" by R.I. Grigorchuk and P.F. Kurchanov. ... Together, these two articles form a wideranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ... In summary, a very interesting book! Bulletin of the London Mathematical Society, 1996 " ... In both essays the authors give clear and comprehensive definitions, examples and statements (but not proofs) of theorems, so that the book can be understood by a reader with a minimal background in group theory or geometry. Such a reader, needing to find out what is known in this area, will find this a full and accessible store of information." Contemporary Physics, 1994 " ... This survey (Part II) presents for the first time that problems in monograph form and by the way offers a unifying treatment of the various approaches to their solutions, as far as they are known, together with hints to open problems. A titbit for every interested reader!" Monatshefte fr Mathematik, 1995
Vokrug Bernsaĭda by
A. I Kostrikin(
Book
)
5 editions published in 1986 in Russian and Undetermined and held by 28 WorldCat member libraries worldwide
5 editions published in 1986 in Russian and Undetermined and held by 28 WorldCat member libraries worldwide
Algebra by
Serge Lang(
Book
)
14 editions published between 1968 and 1996 in 3 languages and held by 27 WorldCat member libraries worldwide
This book is intended as a basic text for a oneyear course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. Comments on Serge Lang's Algebra: Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduatelevel algebra books. April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books. The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra. MathSciNet's review of the first edition
14 editions published between 1968 and 1996 in 3 languages and held by 27 WorldCat member libraries worldwide
This book is intended as a basic text for a oneyear course in Algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. Comments on Serge Lang's Algebra: Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduatelevel algebra books. April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books. The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra. MathSciNet's review of the first edition
Chislovye sistemy by
F. Ė Molin(
Book
)
5 editions published in 1985 in Russian and Undetermined and held by 25 WorldCat member libraries worldwide
5 editions published in 1985 in Russian and Undetermined and held by 25 WorldCat member libraries worldwide
Lineĭnai︠a︡ algebra i geometrii︠a︡ by
A. I Kostrikin(
Book
)
6 editions published between 1980 and 1986 in Russian and held by 16 WorldCat member libraries worldwide
6 editions published between 1980 and 1986 in Russian and held by 16 WorldCat member libraries worldwide
Algebra 8. representations of finitedimensional algebras(
Book
)
4 editions published in 1992 in English and held by 13 WorldCat member libraries worldwide
4 editions published in 1992 in English and held by 13 WorldCat member libraries worldwide
Algebra IX : Finite Groups of Lie Type FiniteDimensional Division Algebras by
A. I Kostrikin(
)
2 editions published in 1996 in English and held by 0 WorldCat member libraries worldwide
The finite groups of Lie type are of central mathematical importance and the problem of understanding their irreducible representations is of great interest. The representation theory of these groups over an algebraically closed field of characteristic zero was developed by P. Deligne and G. Lusztig in 1976 and subsequently in a series of papers by Lusztig culminating in his book in 1984. The purpose of the first part of this book is to give an overview of the subject, without including detailed proofs. The second part is a survey of the structure of finitedimensional division algebras with many outline proofs, giving the basic theory and methods of construction and then goes on to a deeper analysis of division algebras over valuated fields. An account of the multiplicative structure and reduced Ktheory presents recent work on the subject, including that of the authors. Thus it forms a convenient and very readable introduction to a field which in the last two decades has seen much progress
2 editions published in 1996 in English and held by 0 WorldCat member libraries worldwide
The finite groups of Lie type are of central mathematical importance and the problem of understanding their irreducible representations is of great interest. The representation theory of these groups over an algebraically closed field of characteristic zero was developed by P. Deligne and G. Lusztig in 1976 and subsequently in a series of papers by Lusztig culminating in his book in 1984. The purpose of the first part of this book is to give an overview of the subject, without including detailed proofs. The second part is a survey of the structure of finitedimensional division algebras with many outline proofs, giving the basic theory and methods of construction and then goes on to a deeper analysis of division algebras over valuated fields. An account of the multiplicative structure and reduced Ktheory presents recent work on the subject, including that of the authors. Thus it forms a convenient and very readable introduction to a field which in the last two decades has seen much progress
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Related Identities
 Шафаревич, И. Р (Игорь Ростиславович) 1923 Other Honoree Author Editor
 Bokutʹ, L. A. (Leonid Arkadʹevich) 1937 Other Editor
 Manin, I︠U︡. I.
 Мальцев, А. И (Анатолий Иванович) 19091967 Other Dedicatee
 Кутателадзе, С. С (Семен Самсонович) Other Editor
 Paršin, Aleksej N. Editor
 Артамонов, В. А (Вячеслав Александрович) Other
 Gamkrelidze, Revaz V.
 Ershov, Yuri L. Other Editor
 Gamkrelidze, Revaz V.
Useful Links
Associated Subjects
Algebra Algebra, Abstract Algebra, Homological Algebraic varieties Algebras, Linear Associative algebras Burnside problem Combinatorial analysis Combinatorial group theory Determinants Division algebras Finite groups Geometry Geometry, Algebraic Geometry, Analytic Group theory Infinite groups Ktheory Lie groups Linear algebraic groups Line geometry Mathematics Modules (Algebra) Monoids Nonassociative algebras Noncommutative rings Numbers, Complex Number theory Polynomials Representations of algebras Representations of groups Rings (Algebra) Topological groups Vector spaces
Alternative Names
Aleksiej Kostrikin
Alexei Iwanowitsch Kostrikin russischer Mathematiker
Alexei Kostrikin mathématicien russe
Alexei Kostrikin Russian mathematician
Alexei Kostrikin Russisch wiskundige (19292000)
Kostrikin, A.
Kostrikin, A. I.
Kostrikin, A. I. 19292000
Kostrikin, Alekseĭ Ivanovich
Kostrikin, Aleksei Ivanovich 19292000
Kostrikin, Aleksej I.
Kostrikin, Aleksej Ivanovič
Kostrikin, Aleksej Ivanovič 19292000
Kostrikin, Aleksej Ivanovich 19292000
Kostrikin, Aleksiej I.
Kostrikin, Alexei 19292000
Kostrikin, Alexei I.
Kostrikin, Alexei I. 19292000
Kostrikin, Alexei Ivanovich 19292000
Kostrykin, A. I.
Кострикин, Алексей Иванович
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