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

Dirar Benkhadra; Driss Bennis; J. R. Garcia Rozas

paper

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

arXiv:1911.09364

Abstract

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.

arXiv commentTo appear Algebra Colloquium: Volume 27 (2020), Number 3. (Special Issue; proceedings of The International Conference on Algebra and Related Topics; ICART 2018)