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GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY

Published online by Cambridge University Press:  24 June 2010

TOMA ALBU
Affiliation:
‘Simion Stoilow’ Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-010145 Bucharest 1, Romania e-mail: Toma.Albu@imar.ro
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Abstract

In this survey paper we present some results relating the Goldie dimension, dual Krull dimension and subdirect irreducibility in modules, torsion theories, Grothendieck categories and lattices. Our interest in studying this topic is rooted in a nice module theoretical result of Carl Faith [Commun. Algebra27 (1999), 1807–1810], characterizing Noetherian modules M by means of the finiteness of the Goldie dimension of all its quotient modules and the ACC on its subdirectly irreducible submodules. Thus, we extend his result in a dual Krull dimension setting and consider its dualization, not only in modules, but also in upper continuous modular lattices, with applications to torsion theories and Grothendieck categories.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

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