Abelian Groups, Rings and Modules: AGRAM 2000 Conference July 9-15, 2000, Perth, Western Australia
American Mathematical Soc., 2001 - Mathematics - 308 pages
This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings are dedicated to Professor Laszlo Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article. They present recent results from active research areas: Error correcting codes as ideals in group rings, Duality in module categories, Automorphism groups of abelian groups, and Generalizations of isomorphism in torsion-free abelian groups. In addition to these surveys, the volume contains 22 research articles in diverse areas connected with the themes of the conference. The areas discussed include abelian groups and their endomorphism rings, modules over various rings, commutative and non-commutative ring theory, varieties of groups, and topological aspects of algebra. The book offers a comprehensive source for recent research in this active area of study.
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arbitrary assume Aut(G automorphism groups cardinality codes commutative compact completely decomposable group condition contains Corollary cotorsion theory countable cro-group cyclic decomposition Dedekind domain defined denote direct sum direct summand divisible dually slender module End(X endomorphism ring equivalent exact sequence example exists finite rank free module Fuchs group G groups of finite Hausen height sequence Hence homomorphism idempotent implies integral domain Jacobson radical knice subgroup LCA group Lemma Let G Math Noetherian non-zero nonnegative integer p-group p-local prime projective dimension PROOF Proposition Prüfer domain pure independent sets pure subgroup quasi-isomorphic quotient R-module radical regular ring result right ideal satisfies subgroup of G submodule subset TC(C TC(G Theorem topologically pure torsion groups torsion-free abelian groups torsion-free group UDS property valuation domains vector Warfield domains Warfield group wreath product XX-isotype subgroup