Topics in ring theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chicago [u.a.]
Univ. of Chicago Press
1972
|
| Edition: | 2. impr. |
| Series: | Chicago lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 132 S. |
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Record in the Search Index
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| adam_text | CONTENTS
Preface xi
CHAPTER 1. LIE AND JORDAN STRUCTURES
IN SIMPLE RINGS 1
1. Jordan simplicity of R 3
2. Lie structure of R 4
3. A result on rings with involution 10
4. The Lie structures of [R,R] 11
5. Subrings fixed by automorphisms 19
CHAPTER 2. SIMPLE RINGS WITH INVOLUTION . . 25
1. Introduction 25
2. Involutions of the second kind 27
3. The subring generated by the
skew elements 28
4. A theorem of Baxter 29
5. Jordan simplicity of the
symmetric elements 32
6. Lie structures of K, the skew elements. ... 33
7. Lie structure of [K,K] 40
CHAPTER 3. JORDAN HOMOMORPHISMS
AND DERIVATIONS 47
1. Jordan homomorphisms onto
prime rings 47
2. n Jordan mappings 52
3. Jordan derivations 53
vii
viii
4. Another look at Jordan homomorphisms .... 56
5. Some results of Martindale 58
CHAPTER 4. GOLDIE S THEOREMS 61
1. Rings of quotients 61
2. Goldie rings 62
3. Ore domains 63
4. Prime Goldie rings 65
5. First Goldie theorem 70
6. Faith Utumi theorem 72
7. Structure of semi prime Goldie rings 75
8. Principal left ideal rings 7
9. Structure of principal left ideal rings 79
10. The Procesi Small proof of
Goldie s theorem 81
CHAPTER 5. MORE ON RINGS WITH ASCENDING
CHAIN CONDITIONS 87
1. Nil rings satisfying ascending chain
conditions on annihilators 87
2. Nil Goldie rings 92
3. A result on polynomial identities 96
4. Ultra products 97
5. Posner s theorem on prime P.I. rings 101
CHAPTER 6. DECOMPOSITION IN NOETHERIAN
RINGS 105
1. The Lesieur Croisot results 105
2. Tertiary radical 106
3. Tertiary decomposition 111
4. Artin Rees modules 113
ix
CHAPTER 7. RECENT EXAMPLES AND
COUNTER EXAMPLES 115
1. The Golod Shafarevitch theorem 116
2. Counter example to the Kurosh Levitzki
problem 120
3. Counter example to the general Burnside
problem 121
4. Bergman s example of a right but not
left primitive ring 122
5. Sasiada s example of a simple
radical ring 125
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| any_adam_object | 1 |
| author | Herstein, Israel N. |
| author_facet | Herstein, Israel N. |
| author_role | aut |
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| author_variant | i n h in inh |
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| bvnumber | BV013491240 |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)614758024 (DE-599)BVBBV013491240 |
| discipline | Mathematik |
| edition | 2. impr. |
| format | Book |
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| indexdate | 2024-07-09T18:46:45Z |
| institution | BVB |
| language | English |
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| physical | XI, 132 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Univ. of Chicago Press |
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| series2 | Chicago lectures in mathematics |
| spelling | Herstein, Israel N. Verfasser aut Topics in ring theory I. N. Herstein 2. impr. Chicago [u.a.] Univ. of Chicago Press 1972 XI, 132 S. txt rdacontent n rdamedia nc rdacarrier Chicago lectures in mathematics Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009207813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Herstein, Israel N. Topics in ring theory Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4128084-2 |
| title | Topics in ring theory |
| title_auth | Topics in ring theory |
| title_exact_search | Topics in ring theory |
| title_full | Topics in ring theory I. N. Herstein |
| title_fullStr | Topics in ring theory I. N. Herstein |
| title_full_unstemmed | Topics in ring theory I. N. Herstein |
| title_short | Topics in ring theory |
| title_sort | topics in ring theory |
| topic | Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Ring Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009207813&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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