Communications of the
Korean Mathematical Society CKMS

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.

Keywords: Regular injective module, regular injective dimension, regular global dimension, total ring of quotients, Dedekind ring

MSC numbers: 13C11, 13D05

Supported by: The first author was supported by National Natural Science Foundation of China (No. 12201361).