Synopses & Reviews
This volume consists mainly of refereed papers and surveys presented at the 1994 Padova Conference `Abelian Groups and Modules', augmented by a few contributions specifically written for this publication. Linking three main areas in algebra, namely Abelian groups, commutative algebra and modules over non-commutative rings, it gives an excellent survey of current trends as well as state-of-the-art results in specific research topics. Subjects covered include: representation theory, Hopf modules, Krull dimension, dualities, finitistic dimension, algebraically compact modules, von Neumann regular rings, serial rings, reflexive algebras, endomorphism rings, Butler groups, torsion-free Abelian groups, and totally projective groups. Audience: Graduate students and researchers in algebra.
Table of Contents
Preface. Conference information. Dual relative Krull dimension of modules over commutative rings; T. Albu, P.F. Smith. Morita duality, linear compactness and AB5*: a survey; P.N. Ánh. Near isomorphism of Butler groups and representations of finite posets; D.M. Arnold. Locally free finite rank Butler groups and near isomorphism; D.M. Arnold, M. Dugas. Subgroups of Butler groups; L. Bican. Some Abelian groups with free duals; A. Blass, et al. Confirmation of a conjecture of Dans and Hoffmann on biregular rings; W.D. Burgess. Induction factors for the Doi-Koppinen unified Hopf modules; S. Caenepeel, S. Raianu. One-dimensional rings of finite representation type; N. Cimen, et al. Uniqueness of dualities; D. Dikranjan. Classification and non-classification results for Abelian groups; P.C. Eklof. Sigma-pure-injective modules over serial rings; A. Facchini, G. Puninski. Modules over endomorphism rings as homotopy classes; T.G. Faticoni. Categories of mixed and torsion-free finite rank Abelian groups; A. Fomin, W.J. Wickless. Reflexive representation of algebras; K.R. Fuller. Zero-dimensional subrings of commutative rings; R. Gilmer. The dimension of the tensor product of two particular pullbacks; F. Girolami, S.E. Kabbaj. On the existence of ALEPH1-free Abelian groups of cardinality ALEPH1; R. Göbel, S. Shelah. Warfield duality and module extension over a Noetherian domain; H.P. Goeters. Von Neumann regular rings and direct sum decomposition problems; K.R. Goodearl. Selforthogonal modules; D. Happel. Subrings of finite-dimensional rings; W.J. Heinzer. Primary Abelian groups whose countable subgroups have countable closure; P. Hill, C. Megibben. Isotype separable subgroups of totally projective groups; P. Hill, W. Ullery. Representable preradicals with enough projectives; P. Keef. Rings with periodic unit groups; J. Krempa. Abelian groups with contractions II: weak o-minimality; F.V. Kuhlmann. Almost completely decomposable torsion-free Abelian groups; A. Mader. On the exchange property for quasi-continuous modules; S. Mohammed, B.J. Muller. Endomorphism rings of Reid groups; O. Mutzbauer. Completely decomposable subgroups and factors of finite rank completely decomposable groups; L.G. Nongxa, C. Vinsonhaler. On the endomorphism ring of an infinite dimensional vector space; A. Orsatti, N. Rodinò. Some algebraically compact modules I; C.M. Ringel. The near endomorphism ring of an almost completely decomposable group; P. Schulz. Reflexivity of left serial algebras; N. Snashall. On a class of minimal topological modules; A. Tonolo. Steady rings may contain large sets of orthogonal idempotents; J. Trlifaj. The Holy Grail of algebra: seeking complete sets of invariants; P. Vámos. Invariants for almost completely decomposable groups; B.C. Vinsonhaler. A class of modules with semisimple behavior; J.M. Zelmanowitz. The finitistic dimension conjectures &endash; a tale of 3.5 decades; B. Zimmermann Huisgen.