Classical artinian rings and related topics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
World Scientific Publ.
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 291 S. |
| ISBN: | 9789814287241 9814287245 |
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Record in the Search Index
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|---|---|
| adam_text | Titel: Classical artinian rings and related topics
Autor: Baba, Yoshitomo
Jahr: 2009
Contents
Preface vii
List of Symbols xvii
1. Preliminaries 1
1.1 Background Sketch...................... 1
1.2 Semiperfect Rings and Perfect Rings............ 17
1.3 Frobenius Algebras, and Nakayama Permutations and
Nakayama Automorphisms of QF-Rings.......... 27
1.4 Notation in Matrix Representations of Rings ....... 31
2. A Theorem of Fuller. 35
2.1 Improved Versions of Fuller s Theorem........... 36
2.2 M-Simple-Injective and Quasi-Simple-Injective Modules . 49
2.3 Simple-Injectivity and the Condition ar[e, g,f]...... 52
2.4 ACC on Right Annihilator Ideals and the Condition
xr[e,gj}........................... 60
2.5 Injectivity and Composition Length ............ 63
3. Harada Rings 69
3.1 Definition of Harada Rings ................. 69
3.2 A Dual Property of Harada Rings ............. 83
3.3 The Relationships between Harada Rings and Co-Harada
Rings............................. 100
4. The Structure Theory of Left Harada Rings 107
4.1 Left Harada Rings of Types (fl) and (*) .......... 107
xiv Classical Artinian Rings and Related Topics
4.2 A Construction of Left Harada Rings as Upper Staircase
Factor Rings of Block Extensions of QF-Rings....... 108
4.3 The Representation of Left Harada Rings as Upper Stair-
case Factor Rings of Block Extensions of QF-Rings .... 115
5. Self-Duality of Left Harada Rings 139
5.1 Nakayama Isomorphisms, Weakly Symmetric Left #-Rings
and Almost Self-Duality................... 140
5.2 Self-Duality and Almost Self-Duality of Left Harada Rings 142
5.3 Koike s Example of a QF-Ring without a Nakayama Auto-
morphism ........................... 150
5.4 Factor Rings of QF-Rings with a Nakayama Automorphism 153
6. Skew Matrix Rings 157
6.1 Definition of a Skew Matrix Ring.............. 157
6.2 Nakayama Permutations vs Given Permutations...... 163
6.3 QF-Rings with a Cyclic Nakayama Permutation...... 171
6.4 Strongly QF-Rings...................... 183
6.5 Block Extensions of Skew Matrix Rings.......... 187
7. The Structure of Nakayama Rings 191
7.1 Kupisch Series and Kupisch Well-Indexed Set via Left H-
Rings ............................. 192
7.2 Nakayama ÇF-Rings..................... 201
7.3 A Classification of Nakayama Rings ............ 203
7.4 An Example of a Nakayama QF-Ring of KNP(1 - 1)-Type 229
7.5 The Self-Duality of Nakayama Rings............ 232
8. Modules over Nakayama Rings 235
8.1 Characterizations of Nakayama Rings by Lifting and Ex-
tending Properties...................... 235
9. Nakayama Algebras 243
9.1 Nakayama Algebras over Algebraically Closed Fields . . . 243
9.2 Nakayama Group Algebras ................. 250
10. Local QF-rings 261
10.1 Local QF-rings........................ 261
Contents xv
10.2 Examples of Local QF-Rings with Radical Cubed Zero . . 270
Open Questions 275
Bibliography 277
Index 287
|
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| bvnumber | BV035821772 |
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| discipline | Mathematik |
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| isbn | 9789814287241 9814287245 |
| language | English |
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| physical | XVIII, 291 S. |
| publishDate | 2009 |
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| spelling | Baba, Yoshitomo Verfasser aut Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro London [u.a.] World Scientific Publ. 2009 XVIII, 291 S. txt rdacontent n rdamedia nc rdacarrier Artinscher Ring (DE-588)4202669-6 gnd rswk-swf Artinscher Ring (DE-588)4202669-6 s DE-604 Oshiro, Kiyoichi Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018680509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baba, Yoshitomo Oshiro, Kiyoichi Classical artinian rings and related topics Artinscher Ring (DE-588)4202669-6 gnd |
| subject_GND | (DE-588)4202669-6 |
| title | Classical artinian rings and related topics |
| title_auth | Classical artinian rings and related topics |
| title_exact_search | Classical artinian rings and related topics |
| title_full | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_fullStr | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_full_unstemmed | Classical artinian rings and related topics Yoshitomo Baba, Kiyoichi Oshiro |
| title_short | Classical artinian rings and related topics |
| title_sort | classical artinian rings and related topics |
| topic | Artinscher Ring (DE-588)4202669-6 gnd |
| topic_facet | Artinscher Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018680509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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