On the ideal transforms defined by an ideal

Abstract

Let R be a commutative Noetherian ring, I an ideal of R and M an R-module. The ambiguous structure of I-transform functor DI (−) makes the study of its properties attractive. In this paper we gather conditions under which, DI (R) and DI (M) appear in certain roles. It is shown, under these conditions that DI (R) is a Cohen-Macaulay ring, regular ring, · · · and DI (M) can be regarded as a Noetherian, flat, · · ·R-module. We also present a primary decomposition of zero submodule of DI (M) and secondary representation of DI (M).