On almost p-standard system of parameters of idealization and applications

Abstract

Let (R,m) be a Noetherian local ring and M be a finitely generated R-module. In this paper, we construct almost p-standard systems of parameters (a strict subclass of d-sequences) of the idealization R⋉M. As applications, we give a class of Cohen-Macaulay Rees algebras for idealizations, Cohen-Macaulay Rees modules for unmixed modules, and give precise formulas computing all Hilbert coefficients of the idealization with respect to an almost p-standard system of parameters.