Algebras, Rings and Their Representations: Proceedings of the International Conference Lisbon

Catarina Santa-Clara, Alberto Facchini, Kent R. Fuller, Claus Michael Ringel9789812565983, 981-256-598-1

Surveying the most influential developments in the field, this proceedings reviews the latest research on algebras and their representations, commutative and non-commutative rings, modules, conformal algebras, and torsion theories. The volume collects stimulating discussions from world-renowned names including Tsit-Yuen Lam, Larry Levy, Barbara Osofsky, and Patrick Smith.

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Table of contents :
CONTENTS……Page 6
Introduction……Page 8
Antonio Almeida Costa……Page 16
Conference Participants……Page 20
Contributors……Page 28
Some Corefiective Categories of Topological Modules……Page 32
1. Introduction……Page 38
2. Preliminaries……Page 39
3. Characterization of Regularity Conditions on Lie Triple Systems through the Standard Algebra Envelope……Page 41
4. Inheritance of Primeness by Ideals……Page 43
1. Introduction and Preliminaries……Page 48
2. Main results……Page 51
1. Introduction……Page 56
2. On the class of T-divisible modules……Page 58
3. Self-T-divisible modules and direct sums……Page 62
1. Introduction and preliminaries……Page 68
2. Rings for which every locally inner automorphism is inner……Page 70
3. Counterexamples……Page 78
4. Skolem-Noether results……Page 79
Introduction……Page 84
1. Archimedean components of V(R)……Page 89
2. Idempotents archimedean components subgroups of V(R) and Ko(R)……Page 92
3. Krull monoids……Page 94
4. The example of commutative rings……Page 98
1. Introduction……Page 104
2. General Progenerator Sums……Page 105
4. Non-free Progenerator Sum……Page 106
1. Introduction……Page 110
2. Definitions……Page 111
3. Equivalence Classes of 3-Dimensional Lie Algebras……Page 114
4. Versal Deformations and the Moduli Space……Page 116
1. Introduction……Page 124
2. Basic properties of algebras of skew type……Page 127
3. Questions and comments……Page 130
4. Monomial semigroups……Page 134
5. Structural chains……Page 139
1. Background……Page 144
2. Introduction……Page 145
3. Artinian Triads and Drozd Rings……Page 147
4. Dedekind-like Rings……Page 151
5. Local-Global and Direct-Sum Relations……Page 156
6. Mod-r as Approximation to Mod-A……Page 163
7. Module Structure: Complete Local Case……Page 165
8. Module Structure One Special (Complete Local) Case……Page 168
9. Epilog on the Concept “Dedekind-like”……Page 178
1. Introduction……Page 184
2. Different Types of Corner Rings……Page 187
3. Examples of Unital Corners (and Their Complements)……Page 196
4. Split Peirce Corners……Page 201
5. Reduction of Corners and Correspondence of Complements……Page 206
1. PPF for the non-commutative case……Page 214
2. PPF for commutative rings with zero-divisors……Page 217
3. New generalizations of factoriality……Page 223
Introduction……Page 232
1. Basic properties of category O……Page 233
2. Indecomposable projective modules in O0 for sl3(C)……Page 235
3. Morphisms between projective modules in Oo for sl3(C)……Page 238
4. Algebra associated with the principal block Oo for sl3 (C)……Page 241
1. Introduction……Page 246
2. Cohen-Macaulay Algebras……Page 249
3. Gorenstein Algebras……Page 254
4. Geometric Algebras……Page 258
5. Three-dimensional Quantum Polynomial Rings……Page 265
1. Introduction……Page 272
2. Quasideterminants……Page 276
3. The division ring of rational functions……Page 280
4. Van der Monde quasideterminants……Page 281
5. Symmetric functions……Page 288
6. A very brief introduction to the algebra Qn……Page 290
Certains Resultats sur une Extension Minimale……Page 296
1. Basic notions……Page 304
2. The algebra M(2)……Page 306
Introduction……Page 320
1. Basic Definitions and Examples……Page 321
2. Representation Theory of Conformal Algebras……Page 327
3. Cendn and gcn……Page 330
4. Future Developments……Page 338
Actions of Tori and Finite Fans……Page 344
1. Notation……Page 346
2. Fans associated to the action of G……Page 348
3. Fans associated to the action of H on V……Page 351
4. Fans not contained in a half-space……Page 353
5. Finite polytopes……Page 356
Introduction……Page 360
1. The functors……Page 363
2. Borel subalgebras……Page 365
3. Irreducible representations of gl(1 1)……Page 370
4. Parabolic subalgebras……Page 371
5. Final remarks……Page 373
Injective Dimension Relative to a Torsion Theory……Page 374
1. Relative injective dimension……Page 375
2. Special torsion theories……Page 380
3. Examples……Page 383
2. Notation and conventions……Page 388
3. Compact and countably compact rings……Page 390
4. Wedderburn-Malcev decomposition of countably compact rings……Page 395
5. Open questions……Page 400