Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, commutative rings, module and ring theory, and topological algebraic structures—providing more than 600 current references and 570 display equations for further exploration of the topic.
Author(s): Alberto Facchini, Evan Houston, Luigi Salce
Series: Lecture Notes in Pure and Applied Mathematics
Edition: 1
Publisher: CRC Press
Year: 2004
Language: English
Pages: 525
Preface......Page 9
Contents......Page 11
Participants to the Conference......Page 15
Contributors......Page 23
Additive Galois Theory of Modules......Page 29
Finitely Generated and Cogenerated QD Groups......Page 41
Direct Limits of Modules of Finite Projective Dimension......Page 55
Classification of a Class of Almost Completely Decomposable Groups......Page 73
A Polynomial Ring Sampler......Page 83
The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain......Page 91
A Note on Cotilting Modules and Generalized Morita Duality......Page 113
Dualities Induced by Cotilting Bimodules......Page 117
Symmetries and Asymmetries for Cotilting Bimodules......Page 131
A Constructive Solution to the Base Change Decomposition Problem in B(1)-groups......Page 147
On a Property of the Adele Ring of the Rationals......Page 161
On Strong Going-between, Going-down, and Their Universalizations......Page 167
Factorization of Divisorial Ideals in a Generalized Krull Domain......Page 177
Divisorial Multiplication Rings......Page 189
Global Deformations of Lie Algebras......Page 205
Maximal Prime Divisors in Arithmetical Rings......Page 217
On Strongly Flat Modules over Matlis Domains......Page 233
Group Identities on Unit Groups of Group Algebras......Page 247
Forty Years of Commutative Ring Theory......Page 257
Modules Induced from a Normal Subgroup of Prime Index......Page 285
Uniquely Transitive Torsion-free Abelian Groups......Page 299
Generalized E-Rings......Page 319
Butler Modules and Bext......Page 335
Remarks on the Multiplicative Structure of Certain One-dimensional Integral Domains......Page 349
Non-finitely Generated Prime Ideals in Subrings of Power Series Rings......Page 361
Rings with Finitely Many Orbits under the Regular Action......Page 371
Projective Covers and Injective Hulls in Abelian Length Categories......Page 377
Semigroup Rings that are Inside Factorial and their Cale Representation......Page 381
Reduced Modules......Page 393
The Mori Property in Rings with Zero Divisors......Page 407
Minimal Prime Ideals and Generalizations of Factorial Domains......Page 429
Factorizations of Monic Polynomials......Page 439
Monotone Complete Ordered Fields, Generalized Power Series, and Integer Parts......Page 453
On Distance between Finite Rings......Page 459
Affine Pairs......Page 465
When a Super-decomposable Pure-injective Module over a Serial Ring Exists......Page 477
Path Coalgebras of Quivers with Relations and a Tame-wild Dichotomy Problem for Coalgebras......Page 493
On Central Galois Algebras of a Galois Algebra......Page 521
