A homological characterization of Pr\"ufer $v$-multiplication rings
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Let $R$ be a ring and $M$ an $R$-module. Then $M$ is said to be regular $w$-flat provided that the natural homomorphism $I\otimes_R M \rightarrow R\otimes_R M$ is a $w$-monomorphism for any regular ideal $I$. We distinguish regular $w$-flat modules from regular flat modules and $w$-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Pr\"ufer\ $v$-multiplication rings (\PvMR s for short) utilizing the homological properties of regular $w$-flat modules.
Abstract
Let $R$ be a ring and $M$ an $R$-module. Then $M$ is said to be regular $w$-flat provided that the natural homomorphism $I\otimes_R M \rightarrow R\otimes_R M$ is a $w$-monomorphism for any regular ideal $I$. We distinguish regular $w$-flat modules from regular flat modules and $w$-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Pr\"ufer\ $v$-multiplication rings (\PvMR s for short) utilizing the homological properties of regular $w$-flat modules.
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