Basic structures of modern algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Series: | Mathematics and its applications
265 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | IX, 419 S. |
| ISBN: | 0792324595 |
Staff View
MARC
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| 245 | 1 | 0 | |a Basic structures of modern algebra |c by Yuri Bahturin |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a IX, 419 S. | ||
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Record in the Search Index
| _version_ | 1804122676823851008 |
|---|---|
| adam_text | TABLE OF 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 generators 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
v
vi TABLE OF CONTENTS
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. PJ 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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| discipline | Mathematik |
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| id | DE-604.BV008279615 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:17:40Z |
| institution | BVB |
| isbn | 0792324595 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005470688 |
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| owner_facet | DE-12 DE-384 DE-634 DE-11 DE-188 |
| physical | IX, 419 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Bachturin, Jurij A. 1946- Verfasser (DE-588)121656136 aut Basic structures of modern algebra by Yuri Bahturin Dordrecht u.a. Kluwer Acad. Publ. 1993 IX, 419 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 265 Aus dem Russ. übers. Algebra Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s DE-604 Mathematics and its applications 265 (DE-604)BV008163334 265 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005470688&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bachturin, Jurij A. 1946- Basic structures of modern algebra Mathematics and its applications Algebra Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4001156-2 |
| title | Basic structures of modern algebra |
| title_auth | Basic structures of modern algebra |
| title_exact_search | Basic structures of modern algebra |
| title_full | Basic structures of modern algebra by Yuri Bahturin |
| title_fullStr | Basic structures of modern algebra by Yuri Bahturin |
| title_full_unstemmed | Basic structures of modern algebra by Yuri Bahturin |
| title_short | Basic structures of modern algebra |
| title_sort | basic structures of modern algebra |
| topic | Algebra Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005470688&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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