Red-injective modules

Juma Kasozi; David Ssevviiri; Vincent Umutabazi

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arXiv · 1705.06411

Red-injective modules

Juma Kasozi·David Ssevviiri·Vincent Umutabazi

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Abstract

Let $\text{Red}(M)$ be the sum of all reduced submodules of a module $M$. For modules over commutative rings, $\text{Soc}(M)\subseteq \text{Red}(M)$. By drawing motivation from how $\text{Soc}$-injective modules were defined by Amin et. al. in \cite{amin2005}, we introduce $\text{Red}$-injective modules, study their properties and use them to characterize quasi-Frobenius rings and $V$-rings.

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Juma Kasozi, David Ssevviiri, Vincent Umutabazi. 2017-05-18. Red-injective modules. https://arxiv.org/abs/1705.06411

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