Rings Related to Stable Range Conditions (Series in Algebra 11)

Contents......Page 16
Preface......Page 8
Notational Conventions......Page 12
1. Stable Range One......Page 20
1.1 Substitutions of Modules......Page 21
1.2 Products of Three Triangular Matrices......Page 29
1.3 Exchange Rings, I......Page 37
1.4 Exchange Rings, II......Page 47
2.1 Elementary Properties......Page 60
2.2 Extensions and Substitutions......Page 67
2.3 Examples......Page 72
2.4 Goodearl-Menal Condition......Page 77
3.1 Symmetry......Page 88
3.2 Morita Contexts......Page 96
3.3 Right Principal Ideals......Page 102
3.4 Exchange Rings with Artinian Primitive Factors......Page 109
4.1 Matrix Extensions......Page 116
4.2 Related Rings......Page 124
4.3 K1-Groups......Page 126
4.4 Medium Stable Rings......Page 130
5.1 Comparability of Modules......Page 138
5.2 Exchange Rings......Page 144
5.3 Element Factorizations......Page 157
5.4 Matrix Factorizations......Page 161
6. Related Comparability......Page 170
6.1 Related Units......Page 171
6.2 Equivalences......Page 179
6.3 The Morita Invariance......Page 185
6.4 Generalized s-Comparability......Page 200
7. Generalized Stable Rings......Page 212
7.1 Criteria......Page 213
7.2 Diagonal Reduction, I......Page 227
7.3 Diagonal Reduction, II......Page 235
7.4 Invertible Matrices......Page 242
8.1 Matrices and Pseudo-Similarity......Page 254
8.2 Pseudo Substitutions......Page 263
8.3 Completions of Diagrams......Page 269
8.4 Quasi-Projective Modules......Page 276
9.1 Counterexamples......Page 284
9.2 Morita Equivalences......Page 287
9.3 Exchange Conditions......Page 296
9.4 Subdirect Products......Page 301
10. Power-Cancellation......Page 310
10.1 Power-Substitutions......Page 311
10.2 The Finite Exchange Properties......Page 321
10.3 Unit  -Regularity......Page 327
10.4 Stable Power-Substitutions......Page 334
11. Stably Euclidean Rings......Page 344
11.1 Divisible Chain Conditions......Page 345
11.2 2-Stable Range Condition......Page 351
11.3 Commutative Case......Page 355
11.4 Stably Free Modules......Page 364
12.1 Weak Substitutions......Page 380
12.2 Endomorphism Rings......Page 395
12.3 Analogue of Stable Range One......Page 402
12.4 Rectangular Matrices......Page 412
13.1 Strong  -Regularity......Page 424
13.2 Stable Ideals......Page 440
13.3 General Comparability......Page 459
13.4 Separative Regular Ideals......Page 469
14.1 Almost Hermitian Rings, I......Page 488
14.2 Almost Hermitian Rings, II......Page 496
14.3 Strongly Separative Rings......Page 508
14.4 Strongly Separative Ideals......Page 517
15.1 Cleanness in Separative Ideals......Page 530
15.2 Regular Rings in which 2 is Invertible......Page 538
15.3 Cleanness in Exchange Rings......Page 546
15.4 Exchange PB-Ideals......Page 554
16.1 Infinite-Dimensional Linear Transformations, I......Page 560
16.2 Infinite-Dimensional Linear Transformations, II......Page 568
16.3 Clean Matrices......Page 576
16.4 Strong Cleanness......Page 586
17.1 Medium Spaces......Page 608
17.2 Abelian Exchange Rings......Page 619
17.3 K0-Groups......Page 627
17.4 Pierce Spaces......Page 634
Bibliography......Page 648
Index......Page 676