Кострикин, А. И (Алексей Иванович)
Overview
Works:  127 works in 509 publications in 5 languages and 5,427 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Adapter, Translator, Honoree 
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
)
30 editions published between 1986 and 2014 in 3 languages and held by 582 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
30 editions published between 1986 and 2014 in 3 languages and held by 582 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
)
54 editions published between 1977 and 2000 in 6 languages and held by 478 WorldCat member libraries worldwide
54 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 463 WorldCat member libraries worldwide
25 editions published between 1988 and 2005 in English and held by 463 WorldCat member libraries worldwide
Around Burnside by
A. I Kostrikin(
Book
)
19 editions published between 1990 and 2014 in English and held by 382 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 382 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
)
15 editions published in 1991 in English and Undetermined and held by 321 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
15 editions published in 1991 in English and Undetermined and held by 321 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 VI : combinatorial and asymptotic methods of algebra : nonassociative structures by
A. I Kostrikin(
Book
)
19 editions published between 1990 and 2011 in English and held by 309 WorldCat member libraries worldwide
"This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V. A. Ufnarovskij is a survey of various combinatorial methods in infinitedimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Grobner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and PoincareBetti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way." ""NonAssociative Structures" by E. N. Kuz'min and I. P. Shestakov surveys the modern state of the theory of nonassociative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is selfcontained and complete with references to proofs in the literature." "The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics."BOOK JACKET
19 editions published between 1990 and 2011 in English and held by 309 WorldCat member libraries worldwide
"This book contains two contributions: "Combinatorial and Asymptotic Methods in Algebra" by V. A. Ufnarovskij is a survey of various combinatorial methods in infinitedimensional algebras, widely interpreted to contain homological algebra and vigorously developing computer algebra, and narrowly interpreted as the study of algebraic objects defined by generators and their relations. The author shows how objects like words, graphs and automata provide valuable information in asymptotic studies. The main methods emply the notions of Grobner bases, generating functions, growth and those of homological algebra. Treated are also problems of relationships between different series, such as Hilbert, Poincare and PoincareBetti series. Hyperbolic and quantum groups are also discussed. The reader does not need much of background material for he can find definitions and simple properties of the defined notions introduced along the way." ""NonAssociative Structures" by E. N. Kuz'min and I. P. Shestakov surveys the modern state of the theory of nonassociative structures that are nearly associative. Jordan, alternative, Malcev, and quasigroup algebras are discussed as well as applications of these structures in various areas of mathematics and primarily their relationship with the associative algebras. Quasigroups and loops are treated too. The survey is selfcontained and complete with references to proofs in the literature." "The book will be of great interest to graduate students and researchers in mathematics, computer science and theoretical physics."BOOK JACKET
Algebra V : homological algebra by
A. I Kostrikin(
Book
)
16 editions published between 1990 and 1994 in English and held by 283 WorldCat member libraries worldwide
This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic Dmodules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are wellknown researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology
16 editions published between 1990 and 1994 in English and held by 283 WorldCat member libraries worldwide
This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic Dmodules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are wellknown researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology
Algebra VIII : representations of finitedimensional algebras(
Book
)
11 editions published between 1991 and 1992 in English and held by 254 WorldCat member libraries worldwide
11 editions published between 1991 and 1992 in English and held by 254 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 240 WorldCat member libraries worldwide
26 editions published in 1992 in English and held by 240 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 IX : finite groups of Lie type, finitedimensional division algebras by
A. I Kostrikin(
Book
)
6 editions published in 1996 in English and held by 184 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
6 editions published in 1996 in English and held by 184 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
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
Orthogonal decompositions and integral lattices by
A. I Kostrikin(
Book
)
15 editions published between 1994 and 2011 in English and held by 175 WorldCat member libraries worldwide
15 editions published between 1994 and 2011 in English and held by 175 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
)
14 editions published in 1993 in English and held by 112 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
14 editions published in 1993 in English and held by 112 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
Algebra by Peter Gabriel(
Book
)
8 editions published in 1992 in English and held by 82 WorldCat member libraries worldwide
8 editions published in 1992 in English and held by 82 WorldCat member libraries worldwide
Algebra. : Finitedimensional division algebras(
Book
)
7 editions published in 1996 in English and held by 78 WorldCat member libraries worldwide
7 editions published in 1996 in English and held by 78 WorldCat member libraries worldwide
Algebra(
Book
)
5 editions published in 1991 in English and held by 29 WorldCat member libraries worldwide
5 editions published in 1991 in English and held by 29 WorldCat member libraries worldwide
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
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Related Identities
 Шафаревич, И. Р (Игорь Ростиславович) 1923 Other Honoree Dedicatee Author Editor
 Bokutʹ, L. A. (Leonid Arkadʹevich) 1937 Other Author Editor
 Manin, I︠U︡. I.
 Мальцев, А. И (Анатолий Иванович) 19091967 Other Dedicatee
 Paršin, Aleksej N. Editor
 Кутателадзе, С. С (Семен Самсонович) Other Editor
 Pham, Huu Tiep 1963
 Gamkrelidze, Revaz V.
 Артамонов, В. А (Вячеслав Александрович) Other
 Ershov, Yuri L. Other Editor
Useful Links
Associated Subjects
Algebra Algebra, Homological Algebraic topology Algebraic varieties Algebras, Linear Associative algebras Burnside problem Combinatorial analysis Division algebras Finite groups Geometry Geometry, Algebraic Group theory Infinite groups Ktheory Lattice theory Lie algebras Lie groups Linear algebraic groups Mathematics Nonassociative algebras Noncommutative rings Number theory Orthogonal decompositions Representations of algebras Representations of groups Topological groups
Alternative Names
Aleksiej Kostrikin
Alexei Iwanowitsch Kostrikin russischer Mathematiker
Alexei Kostrikin matemático ruso
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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