Geodesic
GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY
Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 19-32

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DOI

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.
DOI : 10.1017/S0017089510000285
Mots-clés : 16P60, 16S90, 18E15, 06C05, 06B35 
ALBU, TOMA. GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY. Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 19-32. doi: 10.1017/S0017089510000285
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     title = {GOLDIE {DIMENSION,} {DUAL} {KRULL} {DIMENSION} {AND} {SUBDIRECT} {IRREDUCIBILITY}},
     journal = {Glasgow mathematical journal},
     pages = {19--32},
     year = {2010},
     volume = {52},
     number = {A},
     doi = {10.1017/S0017089510000285},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000285/}
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