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arXiv · 2404.04610

A note on the localization of generalized injective modules

Xiaolei Zhang
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Abstract

Let $R$ be a ring and $S$ a multiplicative subset of $R$. In this note, we study the localization of $S$-injective modules and $u$-$S$-injective modules under $S$-Noetherian rings and $u$-$S$-Noetherian rings, respectively. The $u$-$S$-absolutely pure property is showed to be preserved under localizations over $S$-coherent rings. Besides, we give an example to show the difference between $S$-injective modules and $u$-$S$-injective modules, and some counter-examples to deny some questions proposed in \cite{B24}.

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Xiaolei Zhang. 2024-04-06. A note on the localization of generalized injective modules. https://arxiv.org/abs/2404.04610

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