Affine maps of state spaces and state spaces of K ₀ groups

作者：Zhu Xiaosheng^*

来源：Mathematica Slovaca, 2013, 63(6): 1209-1226.

DOI：10.2478/s12175-013-0166-6

• affine map
• state space
• K-0 group
• ordered abelian group
• semilocal ring

Let phi be a homomorphism from the partially ordered abelian group (S, v) to the partially ordered abelian group (G, u) with phi(v) = u, where v and u are order units of S and G respectively. Then phi induces an affine map phi* 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 phi* is injective, surjective or bijective. Let R be a semilocal ring with the Jacobson radical J(R) and let pi: R -> R/J(R) be a canonical map. We discuss the affine map (K (0) pi)*. 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), 134-154] and [GOODEARL, K. R.-WARFIELD, R. B., Jr.: State spaces of K (0) of noetherian rings, J. Algebra 71 (1981), 322-378] are extended.

• 单位
  南京大学