Linkage and Intermediate C-Gorenstein Dimensions

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.