Affine maps of state spaces and state spaces of $K₀$ groups

Rok, strany: 2013, 1209 - 1226

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 $π: R\to R/J(R)$ be a canonical map. We discuss the affine map $(K₀π)^*$. 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.: \textit{State spaces, finite algebras, and skew group rings}, J. Algebra \textbf{139} (1991), 134–154] and [GOODEARL, K. R.—WARFIELD, R. B., Jr.: \textit{State spaces of $K₀$ of noetherian rings}, J. Algebra \textbf{71} (1981), 322–378] are extended.

ISO 690:

Zhu, X. 2013. Affine maps of state spaces and state spaces of $K₀$ groups. In Mathematica Slovaca, vol. 63, no.6, pp. 1209-1226. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0166-6

APA:

Zhu, X. (2013). Affine maps of state spaces and state spaces of $K₀$ groups. Mathematica Slovaca, 63(6), 1209-1226. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0166-6