Rings with generalized identities:
This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhale...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1996
|
| Schriftenreihe: | Pure and applied mathematics
196 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Providing novel proofs of existing results, Rings with Generalized Identities puts the theory of generalized identities on a rigorous basis with the use of skew group rings...presents Beidar's determination of the generators of the T-ideal of generalized polynomial identities in (semi)prime rings...furnishes a thorough proof of the generalized Poincare-Birkhoff-Witt theorem for (restricted) differential Lie algebras, making extensive use of the Diamond Lemma...gives a general account of the extended centroid and rings of quotients...covers a recent solution to a long-standing conjecture of Herstein on Lie isomorphisms...and more. |
| Beschreibung: | XI, 522 S. graph. Darst. |
| ISBN: | 0824793250 |
Internformat
MARC
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| 100 | 1 | |a Beidar, Konstantin I. |d 1951- |e Verfasser |0 (DE-588)124594654 |4 aut | |
| 245 | 1 | 0 | |a Rings with generalized identities |c K. I. Beidar ; W. S. Martindale III ; A. V. Mikhalev |
| 264 | 1 | |a New York u.a. |b Dekker |c 1996 | |
| 300 | |a XI, 522 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 196 | |
| 520 | 3 | |a This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Providing novel proofs of existing results, Rings with Generalized Identities puts the theory of generalized identities on a rigorous basis with the use of skew group rings...presents Beidar's determination of the generators of the T-ideal of generalized polynomial identities in (semi)prime rings...furnishes a thorough proof of the generalized Poincare-Birkhoff-Witt theorem for (restricted) differential Lie algebras, making extensive use of the Diamond Lemma...gives a general account of the extended centroid and rings of quotients...covers a recent solution to a long-standing conjecture of Herstein on Lie isomorphisms...and more. | |
| 650 | 4 | |a Anneau avec identitté généralisée | |
| 650 | 7 | |a Anneaux non commutatifs |2 ram | |
| 650 | 4 | |a Théorie Lie | |
| 650 | 4 | |a Théorème Poincaré-Birkhoff-Witt | |
| 650 | 4 | |a Polynomial rings | |
| 650 | 0 | 7 | |a Polynomring |0 (DE-588)4175268-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Polynomring |0 (DE-588)4175268-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Martindale, Wallace S. |d 1930- |e Verfasser |0 (DE-588)133139174 |4 aut | |
| 700 | 1 | |a Michalev, Aleksandr V. |e Verfasser |4 aut | |
| 830 | 0 | |a Pure and applied mathematics |v 196 |w (DE-604)BV000001885 |9 196 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007105195&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007105195 | ||
Datensatz im Suchindex
| _version_ | 1804125124129980416 |
|---|---|
| adam_text | Contents
Preface iii
1 Preliminaries 1
1.1 Basic Notions 1
1.2 Tensor Products and Free Algebras 7
1.3 The Diamond Lemma 13
1.4 Coproducts 24
1.5 Introduction to First Order Logic 34
2 Rings of Quotients 51
2.1 Maximal Right Rings of Quotients 51
2.2 The Two sided and Symmetric Rings of Quotients ... 63
2.3 The Extended Centroid 68
2.4 Rings of Quotients of Coproducts 83
2.5 Derivations and (Anti)automorphisms 86
3 The Method of Orthogonal Completions 97
3.1 Basic Notions and Constructions 98
3.2 Pierce Stalks 110
4 Primitive Rings 129
4.1 Rings of Quotients 129
4.2 Density Theorems 133
4.3 Primitive Rings with Nonzero Socle 139
ix
x CONTENTS
4.4 Generalized Pivotal Monomials 150
4.5 Derivations 153
4.6 Involutions 156
4.7 Automorphisms 169
5 The Poincare Birkhoff Witt Theorem 173
5.1 Lie Algebras 174
5.2 Restricted Lie Algebras 180
5.3 Differential Lie Algebras 186
5.4 Restricted Differential Lie Algebras 197
5.5 A Particular Differential Lie Algebra 206
6 Rings with Generalized Polynomial Identities 211
6.1 Prime GPZ rings 211
6.2 Identities with a Fixed Antiautomorphism 222
6.3 Semiprime £P/ rings 226
6.4 Lifting of GPPs 247
6.5 The T ideal of GPPs 258
6.6 Special GPPs 289
7 T identities of Prime Rings 297
7.1 The Home of T identities 297
7.2 Trivial and Reduced T identities 305
7.3 Related Rings 310
7.4 Linear Formulas 316
7.5 Reduced T identities 321
7.6 The Structure of T identities (Fields) 332
7.7 The Structure of T identities (General Case) 344
7.8 T identities with Coefficients in Qmr 360
7.9 Applications 364
8 T identities of Semiprime Rings 385
8.1 The Algebra U{D{R)) 386
8.2 The Group G(R) 398
8.3 The Home of f identities 417
CONTENTS xi
8.4 Semiprime Rings with T identities 422
9 Applications to Lie Theory 437
9.1 The Structure of K 438
9.2 The Lie Extended Centroid of K 451
9.3 Trilinear Symmetric Mappings 455
9.4 Lie Isomorphisms 471
List of Symbols 487
Bibliography 493
Index 519
|
| any_adam_object | 1 |
| author | Beidar, Konstantin I. 1951- Martindale, Wallace S. 1930- Michalev, Aleksandr V. |
| author_GND | (DE-588)124594654 (DE-588)133139174 |
| author_facet | Beidar, Konstantin I. 1951- Martindale, Wallace S. 1930- Michalev, Aleksandr V. |
| author_role | aut aut aut |
| author_sort | Beidar, Konstantin I. 1951- |
| author_variant | k i b ki kib w s m ws wsm a v m av avm |
| building | Verbundindex |
| bvnumber | BV010647446 |
| callnumber-first | Q - Science |
| callnumber-label | QA251 |
| callnumber-raw | QA251.3 |
| callnumber-search | QA251.3 |
| callnumber-sort | QA 3251.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)33101995 (DE-599)BVBBV010647446 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010647446 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:34Z |
| institution | BVB |
| isbn | 0824793250 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007105195 |
| oclc_num | 33101995 |
| open_access_boolean | |
| owner | DE-739 DE-20 DE-703 DE-19 DE-BY-UBM DE-384 |
| owner_facet | DE-739 DE-20 DE-703 DE-19 DE-BY-UBM DE-384 |
| physical | XI, 522 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Beidar, Konstantin I. 1951- Verfasser (DE-588)124594654 aut Rings with generalized identities K. I. Beidar ; W. S. Martindale III ; A. V. Mikhalev New York u.a. Dekker 1996 XI, 522 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 196 This outstanding reference discusses the latest results concerning the area of non-commutative ring theory known as the theory of generalized identities (GIs) - detailing Kharchenko's results on GIs in prime rings, Chuang's extension to anti-automorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Providing novel proofs of existing results, Rings with Generalized Identities puts the theory of generalized identities on a rigorous basis with the use of skew group rings...presents Beidar's determination of the generators of the T-ideal of generalized polynomial identities in (semi)prime rings...furnishes a thorough proof of the generalized Poincare-Birkhoff-Witt theorem for (restricted) differential Lie algebras, making extensive use of the Diamond Lemma...gives a general account of the extended centroid and rings of quotients...covers a recent solution to a long-standing conjecture of Herstein on Lie isomorphisms...and more. Anneau avec identitté généralisée Anneaux non commutatifs ram Théorie Lie Théorème Poincaré-Birkhoff-Witt Polynomial rings Polynomring (DE-588)4175268-5 gnd rswk-swf Polynomring (DE-588)4175268-5 s DE-604 Martindale, Wallace S. 1930- Verfasser (DE-588)133139174 aut Michalev, Aleksandr V. Verfasser aut Pure and applied mathematics 196 (DE-604)BV000001885 196 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007105195&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beidar, Konstantin I. 1951- Martindale, Wallace S. 1930- Michalev, Aleksandr V. Rings with generalized identities Pure and applied mathematics Anneau avec identitté généralisée Anneaux non commutatifs ram Théorie Lie Théorème Poincaré-Birkhoff-Witt Polynomial rings Polynomring (DE-588)4175268-5 gnd |
| subject_GND | (DE-588)4175268-5 |
| title | Rings with generalized identities |
| title_auth | Rings with generalized identities |
| title_exact_search | Rings with generalized identities |
| title_full | Rings with generalized identities K. I. Beidar ; W. S. Martindale III ; A. V. Mikhalev |
| title_fullStr | Rings with generalized identities K. I. Beidar ; W. S. Martindale III ; A. V. Mikhalev |
| title_full_unstemmed | Rings with generalized identities K. I. Beidar ; W. S. Martindale III ; A. V. Mikhalev |
| title_short | Rings with generalized identities |
| title_sort | rings with generalized identities |
| topic | Anneau avec identitté généralisée Anneaux non commutatifs ram Théorie Lie Théorème Poincaré-Birkhoff-Witt Polynomial rings Polynomring (DE-588)4175268-5 gnd |
| topic_facet | Anneau avec identitté généralisée Anneaux non commutatifs Théorie Lie Théorème Poincaré-Birkhoff-Witt Polynomial rings Polynomring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007105195&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT beidarkonstantini ringswithgeneralizedidentities AT martindalewallaces ringswithgeneralizedidentities AT michalevaleksandrv ringswithgeneralizedidentities |