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 explored. There are two extremal cases, one of which is closely related to the theory of Ulrich modules BHU, GOTWY1, GOTWY2, GTT2, and the other one is closely related to the theory of residually faithful modules and the theory of closed ideals BV.

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