When almost Cohen-Macaulay algebras map into big Cohen-Macaulay modules

TL;DR

This paper investigates the properties of almost Cohen-Macaulay algebras, demonstrating their solidity and exploring conditions under which they become phantom extensions or map into balanced big Cohen-Macaulay modules.

Contribution

It establishes that almost Cohen-Macaulay algebras are solid and identifies specific conditions for their relation to phantom extensions and big Cohen-Macaulay modules.

Findings

Almost Cohen-Macaulay algebras are solid.

Conditions for these algebras to be phantom extensions.

Criteria for mapping into balanced big Cohen-Macaulay modules.

Abstract

In this paper, we show that almost Cohen-Macaulay algebras are solid and in this respect, we seek for some special situation when (a) an almost Cohen-Macaulay algebra will be phantom extension and (b) when it maps into a balanced big Cohen-Macaulay module.