Abstract
AbstractIn 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.
Publisher
Cambridge University Press (CUP)
Reference42 articles.
1. Rings of Quotients
2. Rings and Things and a Fine Array of Twentieth Century Associative Algebra
3. 12. Albu T. and Smith P. F. , Primal, completely irreducible, and primary meet decompositions in modules, Preprint Series of the Institute of Mathematics of the Romanian Academy, Preprint nr. 1/2009.
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1. DIMENSION MODULES AND MODULAR LATTICES;Journal of Algebra and Its Applications;2012-09-26