On a new cotorsion pair

Abstract

In cotorsion theories, the cotorsion pairs $\mathcal{S}\mathcal{F},\mathcal{MC}$ of strongly flat and Matlis-cotorsion modules, and $(\mathcal{F},\mathcal{E}\mathcal{C})$ of flat and Enochs-cotorsion modules play important roles.We introduce a new cotorsion pair that in general lies properly between these two (in the partial order generally accepted for cotorsion pairs), and discuss its properties over commutative rings. In particular, we characterize the commutative rings over which this is a perfect cotorsion pair. Our results may shed more light on the relation between the two old cotorsion pairs.