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GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY

Published online by Cambridge University Press:  24 June 2010

TOMA ALBU
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

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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.

Keywords

16P6016S9018E1506C0506B35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue A: Rings and Modules in Honour of Patrick F. Smith's 65th Birthday , July 2010 , pp. 19 - 32
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

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