Real Algebraic and Analytic Geometry
Submission: 2004, February 13.
Let $A$ be a commutative ring with $1$ and $P(A)$ denote the Prüfer hull of $A$. If $P(A)$ is a von Neumann regular ring then $P(A)=A_S$ with $S:=A\cap P(A)^*$ the intersection of $A$ and the group $P(A)^*$ of all units of $P(A)$. As an application, we show that (1) $A$ is a semihereditary ring if and only if $P(A)$ is a von Neumann regular ring; (2) $A$ is a FPF ring if and only if $P(A)$ is a self-injective ring.
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