Skew group rings which are semi-hereditary orders and Prüfer orders in simple Artinian rings (Q1841204)

Let \(G\) be a finite group acting on the commutative ring \(R\) and let \(R*G\) denote the corresponding skew group ring. If \(I\) is an ideal of \(R\), then \(G_I=\{g\in G\mid I^g=I\}\) is called the decomposition group of \(I\) and its subgroup \(G(I)=\{g\in G_I\mid g\) acts trivially on \(R/I\}\) is the inertial group of \(I\). This paper obtains necessary and sufficient conditions for \(R*G\) to be a prime Goldie ring, a semi-hereditary order in a simple Artinian ring, or a Prüfer order in a simple Artinian ring. Properties of the inertial subgroups of certain prime ideals of \(R\) appear in the statements of these results. (Also submitted to MR).