Some remarks on nonnil-coherent rings and $\phi$-IF rings

Wei Qi; Xiaolei Zhang

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arXiv · 2103.14809

Some remarks on nonnil-coherent rings and $\phi$-IF rings

Wei Qi·Xiaolei Zhang

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Abstract

Let $R$ be a commutative ring. If the nilpotent radical $Nil(R)$ of $R$ is a divided prime ideal, then $R$ is called a $\phi$-ring. In this paper, we first distinguish the classes of nonnil-coherent rings and $\phi$-coherent rings introduced by Bacem and Ali [10], and then characterize nonnil-coherent rings in terms of $\phi$-flat modules and nonnil-FP-injective modules. A $\phi$-ring $R$ is called a $\phi$-IF ring if any nonnil-injective module is $\phi$-flat. We obtain some module-theoretic characterizations of $\phi$-IF rings. Two examples are given to distinguish $\phi$-IF rings and IF $\phi$-rings.

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Wei Qi, Xiaolei Zhang. 2021-03-27. Some remarks on nonnil-coherent rings and $\phi$-IF rings. https://arxiv.org/abs/2103.14809

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