RELATIVE COHERENCE OF RINGS

Let R be a ring and tau a hereditary torsion theory for the category of all left R-modules. A right R-module M is called tau-flat if Tor(1)( M, R/I) = 0 for any tau-finitely presented left ideal I. A left R-module N is said to be tau-f-injective in case Ext(1)( R/I, N) = 0 for any tau-finitely presented left ideal I. R is called a left tau-coherent ring in case every tau-finitely presented left ideal is finitely presented. tau-coherent rings are characterized in terms of, among others, tau-flat and tau-f-injective modules. Some known results are extended.