Ore localization and minimal injective resolutions

TL;DR

This paper investigates the structure of localized Ext modules over certain rings, explores conditions for minimal injective resolutions, and extends results from FBN to Auslander-Gorenstein rings.

Contribution

It provides new descriptions of localized Ext modules and characterizes minimal injective resolutions over a broad class of noetherian rings.

Findings

Structure of localized Ext modules described

Conditions for minimal injective resolutions established

Results extended from FBN to Auslander-Gorenstein rings

Abstract

In this paper, we describe the structure of the localization of Ext^{i}_{R}(R/P,M), where P is a prime ideal and M is a module, at certain Ore sets X. We first study the situation for FBN rings, and then consider matters for a large class of Auslander-Gorenstein rings. We need to impose suitable homological regularity conditions to get results in the more general situation. The results obtained are then used to study the shape of minimal injective resolutions of modules over noetherian rings.