Residually faithful modules and the Cohen–Macaulay type of idealizations

Abstract

The Cohen–Macaulay type of idealizations of maximal Cohen–Macaulay modules over Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of which is related to the theory of Ulrich modules, and the other one is related to the theory of residually faithful modules and closed ideals, developed by Brennan and Vasconcelos.