Overview

This volume consists mainly of refereed papers and surveys presented at the 1994 Padova Conference ""Abelian Groups and Modules"". Linking three main areas in algebra, namely Abelian groups, commutative algebra and modules over non-commutative rings, this work surveys current trends as well as recent 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.

Full Product Details

Author:   Alberto Facchini ,  Claudia Menini
Publisher:   Springer
Imprint:   Springer
Edition:   1995 ed.
Volume:   343
Dimensions:   Width: 17.00cm , Height: 3.00cm , Length: 24.40cm
Weight:   2.070kg
ISBN:  

9780792337560

ISBN 10:   0792337565
Pages:   517
Publication Date:   31 October 1995
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Dual relative Krull dimension of modules over commutative rings.- Morita duality, linear compactness and AB5*: a survey.- Near isomorphism of Butler groups and representations of finite posets.- Locally free finite rank Butler groups and near isomorphism.- Subgroups of Butler groups.- Some abelian groups with free duals.- Confirmation of a conjecture of Dauns and Hofmann on biregular rings.- Induction functors for the Doi-Koppinen unified Hopf modules.- One-dimensional rings of finite representation type.- Uniqueness of dualities.- Classification and non-classification results for abelian groups.- ?-pure-injectivemodules over serial rings.- Modules over endomorphism rings as homotopy classes.- Categories of mixed and torsion-free finite rank abelian groups.- Reflexive representations of algebras.- Zero-dimensional subrings of commutative rings.- The dimension of the tensor product of two particular pullbacks.- On the existence of rigid ?1- free abelian groups of cardinality ?1.- Warfield duality and module extensions over a noetherian domain.- Von Neumann regular rings and direct sum decomposition problems.- Selforthogonal modules.- Subrings of finite-dimensional rings.- Primary abelian groups whose countable subgroups have countable closure.- Isotype separable subgroups of totally projective groups.- Representable preradicals with enough projectives.- Rings with periodic unit groups.- Abelian groups with contractions II: Weak o-minimality.- Almost completely decomposable torsion-free abelian groups.- On the exchange property for quasi-continuous modules.- Endomorphism rings of Reid groups.- Completely decomposable subgroups and factors of finite rank completely decomposable groups.- On the endomorphism ring of an infinite dimensional vector space.- Somealgebraically compact modules I.- The near endomorphism ring of an almost completely decomposable group.- Reflexivity of left serial algebras.- On a class of minimal topological modules.- Steady rings may contain large sets of orthogonal idempotents.- The Holy Grail of Algebra: Seeking complete sets of invariants.- Invariants for almost completely decomposable groups.- A class of modules with semisimple behavior.- The finitistic dimension conjectures — a tale of 3.5 decades.

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