Abstract:Let A denote an Artinian module over a commutative ring R and let be a multiplicatively closed set of nonzero ideals of R. The purpose of this article is to show that the Artinian property of A allows one to develop satisfactory important concepts of -reduction and -closure of an ideal w.r.t. A whose properties reflect some of those of the usual concepts of -reduction and -closure of an ideal in a commutative ring introduced by L. J. Ratliff. Among other things, it is shown that the operation I −→ I A is a sem… Show more
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