تقرير
On $S$-injective modules
| العنوان: | On $S$-injective modules |
|---|---|
| المؤلفون: | Bennis, Driss, Bouziri, Ayoub |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, 13C11, 13C13, 13E99 |
| الوصف: | Let $R$ be a commutative ring with an identity, and $S$ a multiplicative subset of $R$. In this paper, we introduce the notion of $S$-injective modules as a weak version of injective modules. Among other results, we provide an $S$-version of the Baer's characterisation of injective modules. We also give an $S$-version of the Lambek's characterization of flat modules: an $R$-module $M$ is $S$-flat if and only if its character, $Hom_{\mathbb{Z}}(M,\mathbb{Q}/\mathbb{Z})$, is an $S$-injective $R$-module. As applications, we establish, under certain conditions, counterparts of Cheatham and Stone's characterizations for $S$-Noetherian rings using the notion of character modules. Comment: 13 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.02041 |
| رقم الأكسشن: | edsarx.2406.02041 |
| قاعدة البيانات: | arXiv |
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