On the Atomic Dimension in Module Categories

This article is concerned with the study of atomic dimension defined on the category of left modules over a ring R. A module theoretic as well as torsion theoretic characterization of rings with atomic dimension is provided. The atomic and Gabriel dimensions are compared and necessary and sufficient...

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Bibliographic Details
Published in:Communications in algebra 2005-11, Vol.33 (12), p.4679-4692
Main Authors: Pérez, Jaime Castro, Raggi, Francisco, Montes, José Ríos, Berg, John van den
Format: Article
Language:English
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Summary:This article is concerned with the study of atomic dimension defined on the category of left modules over a ring R. A module theoretic as well as torsion theoretic characterization of rings with atomic dimension is provided. The atomic and Gabriel dimensions are compared and necessary and sufficient conditions for these two dimensions to coincide are established.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870500276700