Torsion pairs and related modules over trivial ring extensions

Lixin Mao

doi:10.15672/hujms.1272122

Research Article

Torsion pairs and related modules over trivial ring extensions

Year 2024, Volume: 53 Issue: 5, 1291 - 1304, 15.10.2024

Lixin Mao

https://doi.org/10.15672/hujms.1272122

Abstract

Let $R\ltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$. We first study how to construct torsion pairs over $R\ltimes M$ from torsion pairs over $R$. Some characterizations of finitely generated (presented) modules, flat modules and coherent rings relative to a torsion pair over $R\ltimes M$ are obtained. Then we discuss the transfers of torsion pairs over $R\ltimes M$ to $R$. Finally, some applications are given in Morita context rings.

Keywords

torsion pair , trivial ring extension , Morita context ring

Supporting Institution

NSFC

Project Number

12171230, 12271249

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