In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.

In this paper, we discuss a few simple methods for computing the local topological index and its various analogs vector fields differential forms given on complex varieties with singularities of different types. They are based properties regular meromorphic logarithmic forms, dualizing (canonical) module related constructions. particular, show how to compute Cohen–Macaulay, Gorenstein monomial ...

Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full subcategories of strong and weakly topologized objects and show that each is equivalent to the chu category of the original category with respect to the dualizing obj...

We introduce and study a class of objects that encompasses Christensen Foxby’s semidualizing modules complexes Kubik’s quasi-dualizing modules: the [Formula: see text]-adic complexes. give examples equivalent characterizations these objects, including characterization in terms more familiar property. As an application, we proof existence dualizing over complete local rings does not use Cohen St...