Rees Modules and Reduction of an Ideal Relative to a Noetherian Module

Abstract

Let (A, 𝔪) be a Noetherian local ring, E a non-zero finitely generated A-module, and 𝔟 a proper ideal of A. The aim of this paper is, under some assumptions on𝔟 and E, to clarify a necessary and sufficient condition for the Rees module of E associated to 𝔟 to obtain Cohen-Macaulayness. Also, among other independent results about the reduction number of 𝔟 relative to E, we expand a theorem of Marley.