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The Structure of Countably Generated Projective Modules Over Regular Rings

✍ Scribed by P. Ara; E. Pardo; F. Perera

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 287 KB
Volume: 226
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8156

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✦ Synopsis

We prove that, for every regular ring R, there exists an isomorphism between the monoids of isomorphism classes of finitely generated projective right modules Ž Ž . . Ž . over the rings End R and RCFM R , where the latter denotes the ring of R R countably infinite row-and column-finite matrices over R. We use this result to give a precise description of the countably generated projective modules over simple regular rings and over regular rings satisfying s-comparability.

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This paper explicitly determines the core of a torsion-free, integrally closed module over a two-dimensional regular local ring. It is analogous to a result of Huneke and Swanson which determines the core of an integrally closed ideal. The main result asserts that the core of a finitely generated, t