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Basic structures of modern algebra

Basic structures of modern algebra

Material type
단행본
Personal Author
Bahturin, Yuri
Title Statement
Basic structures of modern algebra / by Yuri Bahturin.
Publication, Distribution, etc
Dordrecht ;   Boston :   Kluwer Academic ,   c1993.  
Physical Medium
ix, 419 p. : ill. ; 25 cm.
Series Statement
Mathematics and its applications ; v. 265
ISBN
0792324595 (acid-free paper)
Bibliography, Etc. Note
Includes bibliographical references and indexes.
Subject Added Entry-Topical Term
Algebra.
000 00900pamuuu200265 a 4500
001 000000013089
005 19940923110946.0
008 930715s1993 ne a b 001 0 eng
010 ▼a 93011839
020 ▼a 0792324595 (acid-free paper)
035 ▼a 93011839
040 ▼a DLC ▼c DLC ▼d DLC
041 1 ▼a eng ▼h rus
050 0 0 ▼a QA155 ▼b .B3513 1993
082 0 0 ▼a 512/.02 ▼2 20
090 ▼a 512.02 ▼b B151bE
100 1 0 ▼a Bahturin, Yuri
240 1 0 ▼a Osnovnye struktury sovremenno? algebry. ▼l English
245 1 0 ▼a Basic structures of modern algebra / ▼c by Yuri Bahturin.
260 0 ▼a Dordrecht ; ▼a Boston : ▼b Kluwer Academic , ▼c c1993.
300 ▼a ix, 419 p. : ▼b ill. ; ▼c 25 cm.
490 1 ▼a Mathematics and its applications ; ▼v v. 265
504 ▼a Includes bibliographical references and indexes.
650 0 ▼a Algebra.
830 0 ▼a Mathematics and its applications (Kluwer Academic Publishers) ; ▼v v. 265.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.02 B151bE Accession No. 111009425 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
Preface = ⅶ
Recommendations to the reader = ⅸ
Introduction = 1
 1. Groups = 1
 2. Rings, fields = 19
 3. Modules and representations = 32
Chapter 1. Commutative algebra = 51
 1. Algebraic and transcendental extensions = 51
 2. Galois theory = 60
 3. Affine rings = 69
 4. Modules over principal ideal rings = 76
 5. Algebraic sets = 86
 6. Normed fields = 95
Chapter 2. Groups = 105
 1. Representations of groups = 105
 2. Periodic groups = 114
 3. Free groups and graphs = 123
 4. Representation of groups by generator and relations = 129
 5. Simple groups = 138
 6. Topological groups = 144
Chapter 3. Associative rings = 157
 1. Radical = 157
 2. Classical semisimple rings = 165
 3. Structure of noetherian rings = 169
 4. Central simple algebras = 175
 5. Complete rings of fractions = 190
Chapter 4. Lie algebras = 199
 1. Linear Lie algebras = 199
 2. Universal enveloping algebra = 208
 3. Magnus theory of free groups = 215
 4. Lie algebras with triangular decomposition = 224
 5. Lie algebras and Lie groups = 235
Chapter 5. Homological algebra = 245
 1. Complexes of modules = 245
 2. Cohomology of groups = 254
 3. Splitting of the radical in a finite-dimensional algebra = 267
 4. Brauer group = 273
 5. Hopf algebras = 280
Chapter 6. Algebraic groups = 289
 1. Hopf algebras and algebraic groups = 289
 2. Action of an algebraic group on a set = 305
 3. Action of an algebraic group by linear operators = 314
 4. Solvable groups = 327
Chapter 7. Varieties of algebras = 335
 1. Universal algebras and varieties = 335
 2. Finite basis problem for identities in groups = 346
 3. PI-algebras = 353
 4. Central polynomials for matrix algebras = 364
Set-theoretic supplement = 375
References = 397
Symbol index = 401
Subject index = 405


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