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.
NSFC
12171230, 12271249
12171230, 12271249
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Project Number | 12171230, 12271249 |
Early Pub Date | January 10, 2024 |
Publication Date | October 15, 2024 |
Published in Issue | Year 2024 Volume: 53 Issue: 5 |