A homological reformulation of the link condition

TL;DR

This paper introduces a homological approach to understanding the link condition between prime ideals, providing new insights into module extensions and the structure of noetherian rings.

Contribution

It offers a homological reformulation of the link condition and applies it to analyze module extensions and the local link structure in noetherian rings.

Findings

Established an equivalent homological condition for prime ideal links.

Answered an open question on module extensions over noetherian rings.

Analyzed the local link structure of prime ideals of small homological height.

Abstract

We prove an equivalent condition for the existence of a link between prime ideals in terms of the structure of a certain cohomology module. We use this formulation to answer an open question regarding the nature of module extensions over one sided noetherian rings. We apply the techniques developed in this paper to the local link structure of prime ideals of small homological height and examine when certain noetherian rings satisfy the density condition.