Affine maps of state spaces and state spaces of K 0 groups
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- 作者：Xiaosheng Zhu (1)
- 关键词：Primary 16A18 ; 16A54 ; 16E20 ; Secondary 18F30 ; 19A49 ; affine map ; state space ; K 0 group ; ordered abelian group ; semilocal ring
- 刊名：Mathematica Slovaca
- 出版年：2013
- 出版时间：December 2013
- 年：2013
- 卷：63
- 期：6
- 页码：1209-1226
- 全文大小：263 KB
- 作者单位：Xiaosheng Zhu (1)
1. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R. China - ISSN：1337-2211
文摘
Let φ be a homomorphism from the partially ordered abelian group (S, v) to the partially ordered abelian group (G, u) with φ(v) = u, where v and u are order units of S and G respectively. Then φ induces an affine map φ* from the state space St(G, u) to the state space St(S, v). Firstly, in this paper, we give some suitable conditions under which φ* is injective, surjective or bijective. Let R be a semilocal ring with the Jacobson radical J(R) and let π: R ?R/J(R) be a canonical map. We discuss the affine map (K 0 π)*. Secondly, for a semiprime right Goldie ring R with the maximal right quotient ring Q, we consider the relations between St(R) and St(Q). Some results from [ALFARO, R.: State spaces, finite algebras, and skew group rings, J. Algebra 139 (1991), 134-54] and [GOODEARL, K. R.-WARFIELD, R. B., Jr.: State spaces of K 0 of noetherian rings, J. Algebra 71 (1981), 322-78] are extended.