Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical counterparts, these dimensions rarely come with practical and robust criteria for finiteness, even over commutative noetherian local rings. Indeed, over such a ring ...

Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...

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...