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K0 of a semilocal ring

✍ Scribed by Alberto Facchini; Dolors Herbera

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 183 KB
Volume: 225
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8092

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✦ Synopsis

Let R be a semilocal ring, that is, R modulo its Jacobson radical J R is artinian. Then K 0 R/J R is a partially ordered abelian group with order-unit, isomorphic to Z n ≤ u , where ≤ denotes the componentwise order on Z n and u is an order-unit in Z n ≤ . Moreover, the canonical projection π: R → R/J R induces an embedding of partially ordered abelian groups with order-unit K 0 π : K 0 R → K 0 R/J R . In this paper we prove that every embedding of partially ordered abelian groups with order-unit G → Z n can be realized as the mapping K 0 π : K 0 R → K 0 R/J R for a suitable hereditary semilocal ring R.

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