The homological properties of regular injective modules
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Let $R$ be a commutative ring. An $R$-module $E$ is said to be regular injective provided that $\Ext_R^1(R/I,E)=0$ for any regular ideal $I$ of $R$. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.
Abstract
Let $R$ be a commutative ring. An $R$-module $E$ is said to be regular injective provided that $\Ext_R^1(R/I,E)=0$ for any regular ideal $I$ of $R$. We first show that the class of regular injective modules have the hereditary property, and then introduce and study the regular injective dimension of modules and regular global dimension of rings. Finally, we give some homological characterizations of total rings of quotients and Dedekind rings.
참고문헌 (13)
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