Abstract

We study the notions of n-hereditary rings and its connection to the classes of finitely n-presented modules, FPn-injective modules, FPn-flat modules and n-coherent rings. We give characterizations of n-hereditary rings in terms of quotients of injective modules and submodules of flat modules, and a characterization of n-coherent using an injective cogenerator of the category of modules. We show two torsion pairs with respect to the FPn-injective modules and the FPn-flat modules over n-hereditary rings. We also provide an example of a B?zout ring which is 2-hereditary, but not 1-hereditary, such that the torsion pairs over this ring are not trivial.