Abelian Groups, Module Theory, and Topology

by Dikranjan; Dikran

• ISBN13: 9780824719371
• ISBN10: 0824719379
• Edition: Illus.
• Format: Nonspecific Binding
• Copyright: 1998-08-21
• Publisher: CRC Press

Summary

With contributions from over fifty distinguished mathematicians from more than 15 countries, this text investigates currently popular topics in abelian group theory. Provides a solution to a longstanding problem on automorphisms of p-groups, and studies endomorphism rings and automorphism groups of torsion-free modules over PIDs and valuation domains. Paper. DLC: Abelian groups.

Table of Contents

Preface	p. iii
Contributors	p. ix
Participants to the Conference	p. xiii
Adalberto Orsatti's Contributions to Mathematics
Adalberto Orsatti's Contribution to Abelian Group Theory	p. 3
Orsatti's Contribution to Module Theory	p. 9
Orsatti's Contribution to Topological Albegra	p. 19
List of Adalberto Orsatti's Publications	p. 31
Research Articles
Global Krull Dimension and Global Dual Krull Dimension of Valuation Rings	p. 37
The Luroth's Theorem for Some Complete Valued Fields	p. 55
AB-5* for Module and Ring Extensions	p. 59
K[subscript 0] of Semiartinian Unit-Regular Rings	p. 69
Idempotents of the Class Semigroup of a Prufer Domain of Finite Character	p. 79
Greatest Common Divisors Generalized	p. 91
On a Problem of Prof. A. Orsatti	p. 105
Subgroups of the Baer-Specker Group with Prescribed Endomorphism Ring and Large Dual	p. 113
Isomorphic Automorphism Groups of Torsion-Free p-adic Modules	p. 125
Strongly Graded Coalgebras and Crossed Coproducts	p. 131
A Theorem on Extensions of Bimodules	p. 143
Commutative Rings with Acc on Irreducible Ideals	p. 157
Self Linearly Compact Rings and Dualities	p. 179
Extensions of Compact Abelian Groups by Discrete Ones and Their Duality Theory, II	p. 205
A Note on Quasi-Duality	p. 227
Endomorphism Rings of Modules Whose Cardinality Is Cofinal to Omega	p. 235
Endomorphism Rings and Automorphism Groups of Separable Torsion-Free Modules over Valuation Domains	p. 249
Torsionless Modules and Rings with Finite Essential Socle	p. 261
Building Noetherian Domains Inside an Ideal-adic Completion	p. 279
G-Minimal Topological Groups	p. 289
An Adjointness Relation for Finite Partition Lattices	p. 301
X-Exchange Rings	p. 311
The Variety of Topological Groups Generated by the Class of All Banach Spaces	p. 319
On Thin Generating Sets in Topological Groups	p. 327
Abelian Topological Groups without Irreducible Banach Representations	p. 343
Cyclic Modules over End(V[subscript D]) Whose Endomorphism Ring Is an Ultrapower of D	p. 351
Criteria of Steadiness	p. 359
Automorphisms Which Determine an Abelian p-Group	p. 373
Dualities and Pure Semisimple Rings	p. 381
Suitable Sets in Products of Topological Groups and in Groups Equipped with the Bohr Topology	p. 389
On a Duality with "Less than Usual" Reflexive Abstract Modules	p. 403
The Roelcke Compactification of Unitary Groups	p. 411
Tilting in Module Categories	p. 421
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