The structure of preenvelopes with respect to maximal Cohen-Macaulay modules

TL;DR

This paper explores the structure of special preenvelopes and envelopes related to maximal Cohen-Macaulay modules, focusing on kernels, cokernels, and coresolutions over Henselian Cohen-Macaulay local rings.

Contribution

It provides new insights into the structure of special preenvelopes and coresolutions with respect to maximal Cohen-Macaulay modules, emphasizing their kernels and cokernels.

Findings

Characterization of kernels and cokernels of special preenvelopes

Structural description of special proper coresolutions

Application to Cohen-Macaulay local rings

Abstract

This paper studies the structure of special preenvelopes and envelopes with respect to maximal Cohen-Macaulay modules. We investigate the structure of them in terms of their kernels and cokernels. Moreover, using this result, we also study the structure of special proper coresolutions with respect to maximal Cohen-Macaulay modules over a Henselian Cohen-Macaulay local ring.