On Gerko's Strongly Tor-independent Modules

TL;DR

This paper extends Gerko's result on strongly Tor-independent modules from Cohen-Macaulay rings to more general non-Cohen-Macaulay rings, providing new insights into the structure of artinian local rings.

Contribution

It generalizes Gerko's theorem to non-Cohen-Macaulay rings, broadening the applicability of the original result.

Findings

Gerko's theorem extended to non-Cohen-Macaulay rings

Strongly Tor-independent modules imply non-vanishing of powers of the maximal ideal

Provides new structural insights into artinian local rings

Abstract

Gerko proves that if an artinian local ring $(R,\mathfrak{m}_R)$ possesses a sequence of strongly Tor-independent modules of length $n$, then $\mathfrak{m}_R^n\neq 0$. This generalizes readily to Cohen-Macaulay rings. We present a version of this result for non-Cohen-Macaulay rings.