Abelian Groups and Modules

On the 26th of November 1992 the organizing committee gathered together, at Luigi Salce's invitation, for the first time. The tradition of abelian groups and modules Italian conferences (Rome 77, Udine 85, Bressanone 90) needed to be kept up by one more meeting. Since that first time it was clear to us that our goal was not so easy. In fact the main intended topics of abelian groups, modules over commutative rings and non commutative rings have become so specialized in the last years that it looked really ambitious to fit them into only one meeting. Anyway, since everyone of us shared the same mathematical roots, we did want to emphasize a common link. So we elaborated the long symposium schedule: three days of abelian groups and three days of modules over non commutative rings with a two days' bridge of commutative algebra in between. Many of the most famous names in these fields took part to the meeting. Over 140 participants, both attending and contributing the 18 Main Lectures and 64 Communications (see list on page xv) provided a really wide audience for an Algebra meeting. Now that the meeting is over, we can say that our initial feeling was right.

Texte du rabat

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. br/ 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. br/ 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. br/ emAudience:/em Graduate students and researchers in algebra.

Contenu
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.