Linkage and Intermediate C-Gorenstein Dimensions

TL;DR

This paper introduces a new framework connecting C-Gorenstein dimensions with linkage theory, providing generalized results that deepen understanding of homological invariants and Serre-like conditions in algebra.

Contribution

It defines intermediate C-Gorenstein dimensions and links them with module linkage, extending existing theories and results in homological algebra.

Findings

Established connections between linkage and homological dimensions.

Generalized Serre-like conditions using intermediate C-Gorenstein dimensions.

Proved new results relating linkage with homological invariants.

Abstract

This paper brings together two theories in algebra that have had been extensively developed in recent years. First is the study of various homological dimensions and what information such invariants can give about a ring and its modules. A collection of intermediate C-Gorenstein dimensions is defined and this allows generalizations of results concerning C-Gorenstein dimension and certain Serre-like conditions. Second is the theory of linkage first introduced by Peskine and Szpiro and generalized to modules by Martinskovsky and Strooker. Using the further generalization of module linkage of Nagel, results are proven connecting linkage with these homological dimensions and Serre-like conditions.