WorldCat Identities

Shafarevich, I. R. (Igorʹ Rostislavovich) 1923-2017

Overview
Works: 268 works in 1,337 publications in 10 languages and 16,148 library holdings
Genres: History  Textbooks 
Roles: Author, Editor, Honoree, Author of introduction, Dedicatee, Other, Contributor
Classifications: QA564, 512
Publication Timeline
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Most widely held works by I. R Shafarevich
Algebra I : basic notions of algebra by I. R Shafarevich( Book )

63 editions published between 1986 and 2014 in 4 languages and held by 805 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
Basic algebraic geometry by I. R Shafarevich( Book )

55 editions published between 1974 and 1997 in 3 languages and held by 779 WorldCat member libraries worldwide

Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions*-as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics
Basic algebraic geometry by I. R Shafarevich( Book )

77 editions published between 1994 and 2016 in 5 languages and held by 752 WorldCat member libraries worldwide

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Khler geometry and Hodge theory. The final section raisesan important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics
Geometries and groups by V. V Nikulin( Book )

31 editions published between 1983 and 1994 in English and Russian and held by 676 WorldCat member libraries worldwide

This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry."
The socialist phenomenon by I. R Shafarevich( Book )

11 editions published between 1980 and 2013 in English and held by 475 WorldCat member libraries worldwide

Discourses on algebra by I. R Shafarevich( Book )

17 editions published between 2002 and 2009 in English and Japanese and held by 389 WorldCat member libraries worldwide

The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry. It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20th century, as well as one of the best mathematical writers
Arithmetic and geometry : papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday by I. R Shafarevich( Book )

29 editions published in 1983 in English and held by 358 WorldCat member libraries worldwide

Algebraic geometry I : algebraic curves, algebraic manifolds and schemes by V. I Danilov( Book )

24 editions published between 1988 and 2007 in English and held by 357 WorldCat member libraries worldwide

This book consists of two parts. The first is devoted to the theory of curves, which are treated from both the analytic and algebraic points of view. Starting with the basic notions of the theory of Riemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem, uniformization and automorphic functions
Number theory II : algebraic number theory by Helmut Koch( Book )

19 editions published in 1992 in English and Italian and held by 318 WorldCat member libraries worldwide

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: " ... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 " ... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Algebra II : noncommutative rings, identities by A. I Kostrikin( Book )

12 editions published in 1991 in English and Undetermined and held by 313 WorldCat member libraries worldwide

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative 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 non-commutative 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 so-called microlocal analysis. The theory of operator algebras (Le
Algebraic geometry IV : linear algebraic groups, invariant theory by A. N Parshin( Book )

27 editions published between 1988 and 2010 in English and held by 311 WorldCat member libraries worldwide

This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of part two, E.B. Vinberg and V.L. Popov, are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics
Number theory I : fundamental problems, ideas and theories by I︠U︡. I Manin( Book )

22 editions published between 1992 and 1995 in English and held by 288 WorldCat member libraries worldwide

This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry
Algebra V : homological algebra by A. I Kostrikin( Book )

13 editions published between 1990 and 1994 in English and held by 274 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 D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known 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
Algebraic geometry II : cohomology of algebraic varieties, algebraic surfaces( Book )

20 editions published between 1994 and 2014 in English and held by 268 WorldCat member libraries worldwide

This EMS volume consists of two parts. The first part is devoted to the exposition of the cohomology theory of algebraic varieties. The second part deals with algebraic surfaces. The authors, who are well-known experts in the field, have taken pains to present the material rigorously and coherently. The book contains numerous examples and insights on various topics. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields
Algebraic geometry III : complex algebraic varieties, algebraic curves and their Jacobians by V. S Kulikov( Book )

15 editions published between 1994 and 2009 in English and held by 249 WorldCat member libraries worldwide

Dealing with the subject of complex algebraic geometry, this work offers a succinct summary of the areas it covers, while providing coverage of certain important fields. It presents an introduction to the work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties
Linear algebra and geometry by I. R Shafarevich( Book )

17 editions published between 2012 and 2014 in English and held by 121 WorldCat member libraries worldwide

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics
Number theory, algebra, and algebraic geometry by A. I Kostrikin( Book )

16 editions published between 1995 and 2004 in English and held by 88 WorldCat member libraries worldwide

Collected mathematical papers by I. R Shafarevich( Book )

17 editions published between 1980 and 2015 in 4 languages and held by 75 WorldCat member libraries worldwide

Teorii︠a︡ chisel by Z. I Borevich( Book )

19 editions published between 1964 and 1985 in Russian and Undetermined and held by 70 WorldCat member libraries worldwide

Basic algebraic geometry by I. R Shafarevich( Book )

22 editions published between 1994 and 2013 in English and German and held by 46 WorldCat member libraries worldwide

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
 
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Geometries and groups
Alternative Names
Chafarevich, I. R.

Chafarevich, Igor Rostislavovich

Chafarevitch, I. 1923-

Chafarevitch, I. R.

Chafarevitch, I. R. 1923-

Chafarevitch, I. R., 1923-2017

Chafarévitch, Igor

Chafarévitch, Igor 1923-

Chafarévitch, Igor 1923-2017

Chafarevitch, Igor R.

Chafarevitch, Igor R. 1923-

Chafarevitch, Igor R. 1923-2017

Chafarevitch, Igor R. (Igor Rostislavovich), 1923-

Chafarevitch, Igor Rostislavovitch.

Chafarevitch Igor Rostislavovitch 1923-....

Chafarevitch, Igor Rostislavovitch 1923-2017

Igor Chafarevitch mathématicien russe

Igor' Rostislavovič Šafarevič matematico sovietico

Igor Rostislawowitsch Schafarewitsch russischer Mathematiker

Igor Șafarevici

Igor Safarevics orosz matematikus

Igor Šafarevitš

Igor Šafarevõtš

Igor Shafarevich matemático ruso

Igor Shafarevich Russian mathematician

Igor Shafarevich Soviet and Russian mathematician

Igor Sjafarevitsj Russisch wiskundige

Igor Sjafarevitsj russisk matematikar

Igor Sjafarevitsj russisk matematiker

Igor Szafariewicz

Šafarevič, I. 1923-

Šafarevič, I. 1923-2017

Šafarevič, I. R.

Šafarevič, I. R. 1923-

Šafarevič, I.R. 1923-2017

Šafarevič, Igorʹ.

Šafarevič, Igor' 1923-

Šafarevič, Igor' 1923-2017

Safarevic, Igor R.

Šafarevič, Igor R. 1923-

Šafarevič, Igor R., 1923-2017

Šafarevič, Igorʹ Rostislavovič

Šafarevič, Igorʹ Rostislavovič 1923-

Šafarevič, Igorʹ Rostislavovič 1923-2017

Șafarevici, I. R. 1923-

Șafarevici, I. R., 1923-2017

Safarevié, Igor 1923-

Schafarewitsch, I.R.

Schafarewitsch, I. R. 1923-

Schafarewitsch, I. R. 1923-2017

Schafarewitsch, Igor.

Schafarewitsch, Igor R.

Schafarewitsch Igor R. 1923-....

Schafarewitsch, Igor R. 1923-2017

Schafarewitsch, Igor Rostislavovitsch 1923-

Shafarevich, I.R.

Shafarevich, I.R. 1923-

Shafarevich, I. R. 1923-2017

Shafarevich, I. R. (Igor Rostislavovich)

Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-

Shafarevich, Igor

Shafarevich, Igor 1923-

Shafarevich, Igor R.

Shafarevich Igor R. 1923-....

Shafarevich, Igor' R. 1923-2017

Shafarevich, Igor' Rostislavich

Shafarevich, Igorʹ Rostislavovich

Shafarevich, Igorʹ Rostislavovich 1923-

Shafarevich, Igorʹ Rostislavovich, 1923-2017

Sjafarevitsj, I.R. 1923-

Sjafarewitsj, I.R. 1923-

Szafariewicz, Igor.

Szafariewicz, Igor 1923-

Szafariewicz, Igor, 1923-2017

Xafarevitx, Igor R. 1923-

Игор Шафаревич

Шафаревич, И. Р 1923-

Шафаревич, И. Р. (Игорь Ростиславович), 1923-2017

Шафаревич, Игор Ростилавович 1923-...

Шафаревич, Игор Ростилавович, 1923-2017

Шафаревич, Игор Ростиславович.

Шафаревич, Игорь 1923-

Шафаревич, Игорь (Игорь Ростиславович), 1923-

Шафаревич, Игорь Ростиславович.

Шафаревич, Игорь Ростиславович 1923-...)

Шафаревич, Игорь Ростиславович, 1923-2017

Шафаревич Ігор Ростиславович

Ігар Расціслававіч Шафарэвіч

이고리 샤파레비치

シャハレビッチ

シャファレヴィッチ

シャファレヴィッチ, イゴール R

伊戈爾·沙發列維奇

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Basic algebraic geometryBasic algebraic geometryGeometries and groupsDiscourses on algebraAlgebraic geometry I : algebraic curves, algebraic manifolds and schemesAlgebraic geometry IV : linear algebraic groups, invariant theoryAlgebra V : homological algebraAlgebraic geometry II : cohomology of algebraic varieties, algebraic surfaces