Gorenstein objects in the n-Trivial extensions of abelian categories

Abstract

Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein projective (resp., injective) objects, by defining a new special class of objects. Then we study the transfer of these properties when passing to an abelian category and its n-trivial extension category and also give a characterization of Gorenstein object over it. We give, at the end, applications of this study on the category of modules over an associative ring and triangular matrix rings.