Rings, modules, and preradicals:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1982
|
| Schriftenreihe: | Lecture notes in pure and applied mathematics
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 241 S. |
| ISBN: | 0824715683 |
Internformat
MARC
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| 264 | 1 | |a New York u.a. |b Dekker |c 1982 | |
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| 490 | 1 | |a Lecture notes in pure and applied mathematics |v 75 | |
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Datensatz im Suchindex
| _version_ | 1804114514115821568 |
|---|---|
| adam_text | CONTENTS
PREFACE iii
CHAPTER 0. PRELIMINARIES 1
CHAPTER I. PRERADICALS AND THEIR PROPERTIES 15
1.1 Basic Definitions and Properties 15
1.2 Hereditary and Cohereditary Preradicals 19
1.3 Stable and Costable Preradicals 25
1.4 Composition of Preradicals 28
1.5 More About Radicals and Idempotent Preradicals 36
1.6 Torsion Submodules and Ideals 40
1.7 Centrally Splitting Preradicals 44
1.8 Preradicals and Change of Rings 46
1.9 Preradicals and Ring Direct Sums, Morita Equivalence
and P Equivalence 49
1.10 The Hereditary Preradicals Z, and Soc 51
1.11 The Radicals P and J 57
CHAPTER II. IDEMPOTENT RADICALS AND TORSION THEORIES 67
11.1 Torsion Theories 67
11.2 Generation of Torsion Theories 71
11.3 Torsion n Theories 74
II.h Some Important Idempotent Radicals and
Torsion Theories 76
CHAPTER III. FILTERS AND RADICAL FILTERS OF LEFT IDEALS 83
111.1 Basic Definitions and Properties 83
111.2 Connections Between Filters and Preradicals 86
111.3 Generation of Filters and Radical Filters 89
IIlA Special Types of Filters and Radical Filters 94
vii
CHAPTER IV. INJECTIVITY AND PROJECTIVITY 101
IV. 1 Inactivity and Projectivity With Respect
to a Pair of Preradicals 101
IV.2 Injectivity and Projectivity With Respect
to a Preradical 111
IV.3 Quasiinjective and Quasiprojective Modules 114
IV.k Rational and Corational Extensions 118
IV.5 Tertiary Decompositions 121
IV.6 Tertiary Decompositions A Continuation 126
IV.7 Pseudoinjective and Pseudoprojective Modules 131
CHAPTER V. SEMIPERFECT AND PERFECT RINGS 135
V.I Idempotents 135
V.2 Semiperfect Rings 140
V.3 Perfect Rings l43
V.U Superhereditary Preradicals and Perfect Rings 150
V.5 Hereditary Preradicals and Semiartinian Rings 152
CHAPTER VI. SPLITTING PROPERTIES 159
VI.1 Costability 159
VI.2 Central Splitting 163
VI.3 Stability 166
VI.k Several Consequences 172
VI.5 Primary Decomposition 178
CHAPTER VII. SPLITTING PROPERTIES A CONTINUATION 185
VII.1 Cyclic Splitting Property 185
VII.2 Finitely Generated Splitting Property
and Bounded Splitting Property 189
VII.3 Splitting Property 195
VIIA Splitting Hereditary Radicals over
Commutative Rings 200
CHAPTER VIII. PRERADICALS AND DIMENSIONS 205
VIII. 1 Idempotent Radicals and Homological Dimensions 205
VIII.2 Homological Dimensions of Torsion and
Torsionfree Classes 208
APPENDIX A. RINGS WITH TRIVIAL ORTHOGONAL Ext THEORIES 213
A.I Basic Properties 213
A.2 Preradicals over Left T Rings 214
A.3 Left T Rings of Types 1 and 2 2l6
A.k Left T Rings of Types 3, h, and 5 217
A.5 Commutative T Rings 218
A.6 Commutative Rings with Trivial Orthogonal ® Theories 219
APPENDIX B. EXAMPLES 221
B.I The Ring Z of Integers 221
B.2 The Ring Z(M of Integers Modulo k 223
B.3 The Ring X of Differential Polynomials 223
B.k The Ring U of Upper Triangular 2x2 Matrices
over Z(2) 224
B.5 The (Z Q) Ring W 225
B.6 The O,l) Ring V 226
B.7 The Rings of Infinite Matrices 227
B.8 Miscellanea 227
BIBLIOGRAPHY 229
INDEX 237
|
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| ctrlnum | (OCoLC)8169440 (DE-599)BVBBV000060674 |
| dewey-full | 512.9/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/4 |
| dewey-search | 512.9/4 |
| dewey-sort | 3512.9 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV000060674 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:07:55Z |
| institution | BVB |
| isbn | 0824715683 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000024280 |
| oclc_num | 8169440 |
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| physical | IX, 241 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Dekker |
| record_format | marc |
| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Bican, Ladislav Verfasser aut Rings, modules, and preradicals L. Bican ; T. Kepka ; P. Němec New York u.a. Dekker 1982 IX, 241 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 75 Modules (Algebra) Radical theory Rings (Algebra) Modul (DE-588)4129770-2 gnd rswk-swf Präradikal (DE-588)4175546-7 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s DE-604 Modul (DE-588)4129770-2 s Präradikal (DE-588)4175546-7 s Kepka, T. Verfasser aut Němec, P. Verfasser aut Lecture notes in pure and applied mathematics 75 (DE-604)BV005871364 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000024280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bican, Ladislav Kepka, T. Němec, P. Rings, modules, and preradicals Lecture notes in pure and applied mathematics Modules (Algebra) Radical theory Rings (Algebra) Modul (DE-588)4129770-2 gnd Präradikal (DE-588)4175546-7 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4129770-2 (DE-588)4175546-7 (DE-588)4128084-2 |
| title | Rings, modules, and preradicals |
| title_auth | Rings, modules, and preradicals |
| title_exact_search | Rings, modules, and preradicals |
| title_full | Rings, modules, and preradicals L. Bican ; T. Kepka ; P. Němec |
| title_fullStr | Rings, modules, and preradicals L. Bican ; T. Kepka ; P. Němec |
| title_full_unstemmed | Rings, modules, and preradicals L. Bican ; T. Kepka ; P. Němec |
| title_short | Rings, modules, and preradicals |
| title_sort | rings modules and preradicals |
| topic | Modules (Algebra) Radical theory Rings (Algebra) Modul (DE-588)4129770-2 gnd Präradikal (DE-588)4175546-7 gnd Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Modules (Algebra) Radical theory Rings (Algebra) Modul Präradikal Ring Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000024280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871364 |
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