K<inf>0</inf> of a Semilocal Ring

Alberto Facchini, Dolors Herbera

Research output: Contribution to journalArticleResearchpeer-review

26 Citations (Scopus)

Abstract

Let R be a semilocal ring, that is, R modulo its Jacobson radical J(R) is artinian. Then K0(R/J(R)) is a partially ordered abelian group with order-unit, isomorphic to (Zn,≤,u), where ≤ denotes the componentwise order on Zn and u is an order-unit in (Zn,≤). Moreover, the canonical projection π: R→R/J(R) induces an embedding of partially ordered abelian groups with order-unit K0(π): K0(R)→K0(R/J(R)). In this paper we prove that every embedding of partially ordered abelian groups with order-unit G→Zn can be realized as the mapping K0(π): K0(R)→K0(R/J(R)) for a suitable hereditary semilocal ring R. © 2000 Academic Press.
Original languageEnglish
Pages (from-to)47-69
JournalJournal of Algebra
Volume225
DOIs
Publication statusPublished - 1 Mar 2000

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