arXiv subjects

Dirar Benkhadra

Publications and source records attributed to Dirar Benkhadra.

2 recordsLinked to original sources

arXiv2024

Gorenstein objects in the n-Trivial extensions of abelian categories

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.

math.KT↗

arXiv2020

The category of modules on an n-trivial extension: the basic properties

In this paper we investigate a categorical aspect of $n$-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) $n$-trivial extension of a category by a family of endofunctors. Among other results, projective, injective and flat objects of this category are characterized. We end the paper with two applications. We characterize when an $n$-trivial extension ring is $k$-perfect and we establish a result on the selfinjective dimension of an $n$-trivial extension ring.

math.CT↗