Weak ideal invariance and orders in Artinian rings

Abstract

It Is known that a ring R with Krull dimension is an order in an Artinian ring if R is K-homogeneous and the prime radical N of R is weakly ideal invariant. The notion of weak ideal invariance can be interpreted in torsion theoretic terms, yielding a shorter and more conceptual proof of this result. In addition, it is shown that the orders in Artinian rings which arise in this fashion are precisely those for which R/N is K-homogeneous.