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- W2151807953 abstract "We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M. Moreover, M/tM is a projective module which is isomorphic to a direct sum of finitely generated ideals. These ideals allow us to define a finitely generated ideal whose isomorphism class is an invariant of M. The idempotents and the positive integers defined by the rank of M/tM are invariants of M too. It follows that each semihereditary ring of Krull-dimension one or of finite character, in particular each hereditary ring, has the stacked base property. These results were already proved for Prüfer domains by Brewer, Katz, Klinger, Levy, and Ullery. It is also shown that every semihereditary Bézout ring of countable character is an elementary divisor ring." @default.
- W2151807953 created "2016-06-24" @default.
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- W2151807953 date "2007-09-12" @default.
- W2151807953 modified "2023-10-06" @default.
- W2151807953 title "Finitely Presented Modules Over Semihereditary Rings" @default.
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- W2151807953 doi "https://doi.org/10.1080/00927870701353134" @default.
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