Tensor products and direct limits of almost Cohen-Macaulay modules

TL;DR

This paper studies how the almost Cohen-Macaulay property and Serre conditions behave under tensor products and direct limits in noetherian algebras and modules, revealing their stability and transfer properties.

Contribution

It provides new results on the preservation of almost Cohen-Macaulay and Serre conditions under tensor products and direct limits, extending understanding of these properties in algebraic structures.

Findings

Permanence of almost Cohen-Macaulay property under tensor products

Stability of Serre conditions in direct limits

Conditions for transfer of properties in noetherian algebras

Abstract

We investigate the almost Cohen-Macaulay property and the Serre-type condition $(C_n),\ n\in\mathbb{N},$ for noetherian algebras and modules. More precisely, we find permanence properties of these conditions with respect to tensor products and direct limits.