Кострикин, А. И (Алексей Иванович)
Overview
Works:  94 works in 490 publications in 5 languages and 5,250 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Editor, Other, Adapter, Honoree, Translator 
Classifications:  QA155, 512 
Publication Timeline
.
Most widely held works by
А. И Кострикин
Algebra by
B. L. van der Waerden(
Book
)
61 editions published between 1968 and 2014 in 3 languages and held by 820 WorldCat member libraries worldwide
Contains a tutorial to help master the fundamental concepts of Algebra from monomials, inequalities, and coordinate geometry to functions and variations and word problems
61 editions published between 1968 and 2014 in 3 languages and held by 820 WorldCat member libraries worldwide
Contains a tutorial to help master the fundamental concepts of Algebra from monomials, inequalities, and coordinate geometry to functions and variations and word problems
Introduction to algebra by
Peter J Cameron(
Book
)
72 editions published between 1977 and 2012 in 6 languages and held by 497 WorldCat member libraries worldwide
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters, . new material on axiom of Choice, pgroups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.  ;Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynom
72 editions published between 1977 and 2012 in 6 languages and held by 497 WorldCat member libraries worldwide
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters, . new material on axiom of Choice, pgroups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics.  ;Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynom
Linear algebra and geometry by
A. I Kostrikin(
Book
)
38 editions published between 1980 and 2007 in 4 languages and held by 484 WorldCat member libraries worldwide
38 editions published between 1980 and 2007 in 4 languages and held by 484 WorldCat member libraries worldwide
Algebra II : noncommutative rings, identities by
A. I Kostrikin(
Book
)
30 editions published in 1991 in English and Undetermined and held by 390 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
30 editions published in 1991 in English and Undetermined and held by 390 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
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 VIII : representations of finitedimensional algebras by
Peter Gabriel(
Book
)
27 editions published between 1990 and 1992 in English and held by 344 WorldCat member libraries worldwide
27 editions published between 1990 and 1992 in English and held by 344 WorldCat member libraries worldwide
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 311 WorldCat member libraries worldwide
19 editions published between 1990 and 2011 in English and held by 311 WorldCat member libraries worldwide
Methods of homological algebra by
S. I Gelʹfand(
Book
)
24 editions published between 1990 and 1999 in English and held by 289 WorldCat member libraries worldwide
Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections
24 editions published between 1990 and 1999 in English and held by 289 WorldCat member libraries worldwide
Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections
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 245 WorldCat member libraries worldwide
26 editions published in 1992 in English and held by 245 WorldCat member libraries worldwide
Orthogonal decompositions and integral lattices by
A. I Kostrikin(
Book
)
12 editions published in 1994 in English and held by 175 WorldCat member libraries worldwide
12 editions published in 1994 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
)
15 editions published between 1995 and 1996 in English and held by 153 WorldCat member libraries worldwide
15 editions published between 1995 and 1996 in English and held by 153 WorldCat member libraries worldwide
Vokrug Bernsaĭda by
A. I Kostrikin(
Book
)
5 editions published in 1986 in Russian and Undetermined and held by 26 WorldCat member libraries worldwide
5 editions published in 1986 in Russian and Undetermined and held by 26 WorldCat member libraries worldwide
The number systems; foundations of algebra and analysis by
Solomon Feferman(
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
Combinatorial group theory and applications to geometry by D.J Collins(
Book
)
3 editions published between 1991 and 1998 in English and held by 21 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 21 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
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Related Identities
 Шафаревич, И. Р (Игорь Ростиславович) 1923 Other Honoree Dedicatee Author Editor
 Bokutʹ, L. A. (Leonid Arkadʹevich) 1937 Other 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
 Артамонов, В. А (Вячеслав Александрович) Other
 Gamkrelidze, Revaz V.
 Ershov, Yuri L. Other Editor
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Associated Subjects
Algebra Algebra, Abstract Algebra, Homological Algebraic topology Algebraic varieties Algebras, Linear Associative algebras Burnside problem Categories (Mathematics) Combinatorial analysis Combinatorial group theory Determinants Dmodules Geometry Geometry, Algebraic Geometry, Analytic Group theory Ktheory Lattice theory Lie algebras Line geometry Mathematics Modules (Algebra) Monoids Nonassociative algebras Noncommutative rings Numbers, Complex Number theory Orthogonal decompositions Polynomials Representations of algebras Rings (Algebra) Shmidt, Otto I︠U︡lʹevich, 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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