Some characterizations of rings whose regular ideals are G -projective

Abstract

Abstract In this paper, regular modules are introduced to characterize rings whose regular ideals are G -projective, called G -Dedekind rings, i.e., R is a G -Dedekind ring if and only if any regular R -module is a G -projective R -module; if and only if R / aR is a QF ring for any regular element a in R ; if and only if R is an r -Noetherian ring and every regular prime ideal (or every regular maximal ideal) of R is G -projective.