The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory - ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research.
Author(s): J. L. S. Chen, N. Q. Ding
Publisher: World Scientific Pub Co (
Year: 2008
Language: English
Pages: 335
CONTENTS......Page 8
PREFACE......Page 6
1. Introduction.......Page 12
2. Preliminaries......Page 13
3. Structure of Harada rings of a component type......Page 16
4. Self-duality of Harada ring of a component type......Page 19
References......Page 22
Ring Hulls of Extension Rings Gary F. Birkenmeier, Jae Keol Park and S. Tariq Rizvi......Page 23
References......Page 34
Constructing Morphic Rings Jianlong Chen, Yuanlin Li and Yiqiang Zhou......Page 37
References......Page 43
1. Introduction......Page 44
2. Results......Page 46
References......Page 51
1. The definition and introduction......Page 52
2. Decompositions which complement summands......Page 53
3. The exchange property......Page 56
4. Extending modules......Page 58
5. Lifting, quasi-discrete and discrete modules......Page 61
6. Final remarks......Page 62
References......Page 63
2. Preliminaries and Background......Page 66
3.3 Proposition:......Page 68
3.5 Lemma:......Page 69
4 Symbolic Powers......Page 70
4.3 Theorem [4, Theoreml6J:......Page 71
References......Page 72
1. Projectivity of simple modules......Page 74
2. Flatness of simple modules......Page 75
3. Injectivity of simple modules......Page 76
4. Semiartinian rings and max rings......Page 79
5. -V rings......Page 81
6. Rings whose modules of finite length are semisimple......Page 83
References......Page 84
On a Finitely Generated P-injective Left Ideal Yasuyuki Hirano and Jin Yong Kim......Page 88
References......Page 93
Crossed Products and Fully Prime Rings Liujia Huang and Zhong Yi......Page 95
References......Page 103
1 Nakayama isomorhphism......Page 105
References......Page 115
Introduction......Page 117
1. Matrix Congruence......Page 118
2. k-algebras of Type (l,n, 1)......Page 123
3. k-algebras of Type (1, 2,1)......Page 127
References......Page 128
1. Preliminaries......Page 129
2. Classical Artinian Rings......Page 131
3. Generalized Projectivity......Page 132
4. Direct sums of lifting modules......Page 133
5. Lifting modules over right perfect rings......Page 136
References......Page 138
1. Preliminaries......Page 140
2. Regular Rings with S-comparability......Page 141
3. Weak Comparability......Page 144
4. New Constructions......Page 146
References......Page 148
Semilattice Graded Weak Hopf Algebra and its Quantum Double Fang Li and Haijun Cao......Page 150
1. Decomposition......Page 151
2. Structure Of Quantum Double......Page 155
References......Page 161
1. Introduction......Page 162
2. Results......Page 165
Acknowledgments......Page 176
References......Page 177
1. MORPHIC MODULES......Page 178
2. ENDOMORPHISM RINGS......Page 182
3. LEFT SPECIAL RINGS......Page 184
4. MATRIX RINGS......Page 186
5. STRUCTURE THEOREMS......Page 187
6. INTERNAL CANCELLATION......Page 190
References......Page 191
Clean Rings: A Survey W. K. Nicholson and Yiqiang Zhou......Page 192
1. Connections with other notions......Page 193
2. Clean endomorphism rings......Page 194
4. Strongly clean rings......Page 197
5. Uniquely clean rings......Page 199
6. Group rings......Page 201
7. The extension questions of clean and strongly clean rings......Page 202
8. Semiboolean rings......Page 205
9. Connections with C*-Algebras and clean rings of continuous functions......Page 206
References......Page 208
1. Introduction......Page 210
2. The result......Page 212
References......Page 219
1. Introduction......Page 220
3. Galois Extensions......Page 221
References......Page 225
1. Introduction......Page 226
2. Definitions and Examples......Page 228
3. A Characterization of Regular Coherent Local Rings......Page 230
4. A Generalization of Serre's Theorem......Page 233
References......Page 235
1. Introduction and Preliminaries......Page 236
2. Baer Rings......Page 238
3. Baer Modules......Page 242
4. Connections to Extending Property......Page 245
5. Applications......Page 246
References......Page 251
1. Introduction......Page 253
2. Graded Regularity......Page 255
3. Graded Jacobson Radical......Page 257
4. Graded Direct Finiteness......Page 259
References......Page 261
1. Introduction......Page 262
2. The power-substitution property......Page 263
3. The unit power-substitution property......Page 268
References......Page 273
1.2. Coalgebras and comodules.......Page 274
1.4. Group algebras and their dual.......Page 275
1.6. Corings and comodules.......Page 276
1.7. A as a C-comodule.......Page 277
1.8. Coring of a projective module.......Page 278
1.10. Entwining structures.......Page 279
1.14. Relative injectivity.......Page 280
2.1. Galois Reid extension.......Page 281
2.2. Comodule algebras.......Page 282
2.3. Coalgebra-Galois extensions.......Page 283
2.4. Galois corings.......Page 284
2.5. Hopf algebras.......Page 285
2.6. Galois comodules.......Page 286
3.1. Galois comodules.......Page 287
3.3. (C, .A)-injective modules.......Page 288
3.5. Semisimple Galois comodules.......Page 289
3.7. Strongly (C, A)-injective Galois comodules.......Page 290
References......Page 291
1. A brief recall of the history......Page 293
2. Connection with other conjectures......Page 294
3. Some known results......Page 295
4.2. New results......Page 298
4.3. Remarks......Page 300
4.4. Examples......Page 301
4.5. Some results on representation dimension......Page 302
Acknowledgments......Page 303
References......Page 304
1. Introduction......Page 306
2.2. Covering functors......Page 307
2.3. Repetitive categories......Page 308
3.1. Periodic categories......Page 310
3.2. Positive Galois coverings of self-injective algebras......Page 311
4. Criterion Theorems......Page 313
References......Page 316
Introduction......Page 318
1. Finite dimensional integrable highest weight modules......Page 319
2. The Clebsch-Gordan decomposition......Page 324
References......Page 327
1. introduction......Page 328
2. Main Results......Page 329
References......Page 335
