Automorphisms and derivations of associative rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1991
|
| Series: | Mathematics and its applications / Soviet series
69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 385 S. |
| ISBN: | 0792313828 |
Staff View
MARC
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| 100 | 1 | |a Charčenko, V. K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Automorphisms and derivations of associative rings |c by V. K. Kharchenko. Transl. from the Russian by L. Yuzina |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
| 300 | |a XIV, 385 S. | ||
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Record in the Search Index
| _version_ | 1804119567489826816 |
|---|---|
| adam_text | TABLE OF CONTENTS
INTRODUCTION xi
CHAPTER 1. STRUCTURE OF RINGS
1.1 Baer Radical and Semiprimeness 1
1.2 Automorphism Groups and Lie Differential Algebras 6
1.3 Bergman Isaacs Theorem. Shelter Integrality 11
1.4 Martindale Ring of Quotients 19
1.5 The Generalized Centroid of a Semiprime Ring 24
1.6 Modules over a Generalized Centroid 27
1.7 Extension of Automorphisms to a Ring of Quotients. Conjugation Modules 40
1.8 Extension of Derivations to a Ring of Quotients 50
1.9 The Canonical Sheaf of a Semiprime Ring 53
1.10 Invariant Sheaves 62
1.11 The Metatheorem 65
1.12 Stalks of Canonical and Invariant Sheaves 77
1.13 Martindale s Theorem 81
1.14 Quite Primitive Rings 87
1.15 Rings of Quotients of Quite Primitive Rings 92
CHAPTER 2. ON ALGEBRAIC INDEPENDENCE OF
AUTOMORPHISMS AND DERIVATIONS
2.0 Trivial Algebraic Dependences 96
2.1 The Process of Reducing Polynomials 98
2.2 Linear Differential Identities with Automorphisms 103
2.3 Multilinear Differential Identities with Automorphisms 109
2.4 Differential Identities of Prime Rings 112
2.5 Differential Identities of Semiprime Rings 122
2.6 Essential Identities 126
2.7 Some Applications: Galois Extentions of Pi Rings;
Algebraic Automorphisms and Derivations; Associative
Envelopes of Lie Algebras of Derivations 133
CHAPTER 3. THE GALOIS THEORY OF PRIME RINGS
(THE CASE OF AUTOMORPHISMS)
3.1 Basic Notions 142
3.2 Some Properties of Finite Groups of Outer Automorphisms 144
3.3 Centralizers of Finite Dimensional Algebras 146
3.4 Trace Forms 157
3.5 Galois Groups 160
3.6 Maschke Groups. Prime Dimensions 163
3.7 Bimodule Properties of Fixed Rings 170
3.8 Ring of Quotients of a Fixed Ring 174
3.9 Galois Subrings for M Groups 176
x TABLE OF CONTENTS
3.10 Correspondence Theorems 190
3.11 Extension of Isomorphisms 193
CHAPTER 4. THE GALOIS THEORY OF PRIME RINGS
(THE CASE OF DERIVATIONS)
4.1 Duality for Derivations in the Multiplication Algebra 202
4.2 Transformation of Differential Forms 206
4.3 Universal Constants 209
4.4 Shirshov Finiteness 213
4.5 The Correspondence Theorem 216
4.6 Extension of Derivations 221
CHAPTER 5. THE GALOIS THEORY OF SEMIPRIME RINGS
5.1 Essential Trace Forms 228
5.2 Intermediate Subrings 231
5.3 The Correspondence Theorem for Derivations 234
5.4 Basic Notions of the Galois Theory of Semiprime Rings
(the case of automorphisms) 236
5.5 Stalks of an Invariant Sheaf for a Regular Group.
Homogenous Idempotents 241
5.6 Principal Trace Forms 253
5.7 Galois Groups 257
5.8 Galois Subrings for Regular Closed Groups 258
5.9 Correspondence and Extension Theorems 265
5.10 Shirshov Finiteness. The Structure of Bimodules 266
CHAPTER 6. APPLICATIONS
6.1 Free Algebras 270
6.2 Noncommutative Invariants 280
6.3 Relations of a Ring with Fixed Rings 292
A. Radicals of Algebras 293
B. Units, Semisimple Artinian Rings, Essential
Onesided Ideals 298
C. Primitive Rings 300
D. Quite Primitive Rings 306
E. Goldie Rings 309
F. Noetherian Rings 313
G. Simple and Subdirectly Indecomposable Rings 315
H. Prime Ideals. Montgomery Equivalence 318
I. Modular Lattices 327
J. The Maximal Ring of Quotients 336
6.4 Relations of a Semiprime Ring with Ring of Constants 345
6.5 Hopf Algebras 355
REFERENCES 371
INDEX 383
|
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| id | DE-604.BV005346941 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:28:15Z |
| institution | BVB |
| isbn | 0792313828 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003350950 |
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| physical | XIV, 385 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Charčenko, V. K. Verfasser aut Automorphisms and derivations of associative rings by V. K. Kharchenko. Transl. from the Russian by L. Yuzina Dordrecht [u.a.] Kluwer 1991 XIV, 385 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 69 Automorphismus (DE-588)4143709-3 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s Automorphismus (DE-588)4143709-3 s DE-604 Soviet series Mathematics and its applications 69 (DE-604)BV004708148 69 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003350950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Charčenko, V. K. Automorphisms and derivations of associative rings Automorphismus (DE-588)4143709-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4143709-3 (DE-588)4128084-2 |
| title | Automorphisms and derivations of associative rings |
| title_auth | Automorphisms and derivations of associative rings |
| title_exact_search | Automorphisms and derivations of associative rings |
| title_full | Automorphisms and derivations of associative rings by V. K. Kharchenko. Transl. from the Russian by L. Yuzina |
| title_fullStr | Automorphisms and derivations of associative rings by V. K. Kharchenko. Transl. from the Russian by L. Yuzina |
| title_full_unstemmed | Automorphisms and derivations of associative rings by V. K. Kharchenko. Transl. from the Russian by L. Yuzina |
| title_short | Automorphisms and derivations of associative rings |
| title_sort | automorphisms and derivations of associative rings |
| topic | Automorphismus (DE-588)4143709-3 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Automorphismus Ring Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003350950&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
| work_keys_str_mv | AT charcenkovk automorphismsandderivationsofassociativerings |