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

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

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arXiv · 1911.09364

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

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

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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.

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Dirar Benkhadra, Driss Bennis, J. R. Garcia Rozas. 2019-11-21. The category of modules on an n-trivial extension: the basic properties. https://arxiv.org/abs/1911.09364

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