In this article, we introduce an invariant of Cohen-Macaulay local rings in terms the reduction number canonical ideals. The can be defined arbitrary and it measures how close to being Gorenstein. First, clarify relation between almost Gorenstein nearly by using dimension one. We next characterize idealization trace ideals over invariant. It provides better prospects for a result on property id...

We find new classes of non noetherian rings which have the same homological behavior that Gorenstein rings.

We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answe...

The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, infinitely tilting have recently studied many authors context Gorenstein homological algebra. In this work, we build on developing “Gorenstein approximations” employing these approximations to study classes their associated cotorsion pairs. As applications our results, discu...