Big projective modules over noetherian semilocal rings

Dolors Herbera, Pavel Přhoda

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

We prove that for a noetherian semilocal ring R with exactly k isomorphism classes of simple right modules the monoid V*(R) of isomorphism classes of countably generated projective right (left) modules, viewed as a submonoid of V*(R/J(R)), is isomorphic to the monoid of solutions in (ℕ0 ∪ {∞})k of a system consisting of congruences and diophantine linear equations. The converse also holds, that is, if M is a submonoid of (ℕ0∪{∞})k containing an order unit (n1, ⋯ , nk) of ℕ k0which is the set of solutions of a system of congruences and linear diophantine equations then it can be realized as V*(R) for a noetherian semilocal ring such that R/J(R) ≅ Mn1(D1) × ⋯ × Mnk (Dk) for suitable division rings D1, ⋯ , Dk. © 2010 Walter de Gruyter Berlin · New York.
Original languageEnglish
Pages (from-to)111-148
JournalJournal fur die Reine und Angewandte Mathematik
Issue number648
DOIs
Publication statusPublished - 1 Nov 2010

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