Gorenstein Dimension over Some Rings of the Form R [0 plus]C

Abstract

Commutative algebra is the study of commutative rings and other abstract structures based on commutative rings. Modules can be viewed as a common generalization of several of those structures, and some invariants, e.g. homological dimensions, of modules are used to characterize certain properties of the base ring. Some generalizations of such invariants include C-Gorenstein dimensions, where C is a semidualizing module over a commutative noetherian ring. Holm and Jørgensen [16] investigate some connections between C-Gorenstein dimensions of an R-complex and Gorenstein dimensions of the same complex viewed as a complex over the "trivial extension" R × C. I generalize some of their results to a certain type of retract diagram. I also investigate some examples of such retract diagrams, namely D'Anna and Fontana's amalgamated duplication [8] and Enescu's pseudocanonical cover [9].