Some properties of associate and presimplifiable rings

Abstract

In this paper we study some properties of associate and presimplifiable rings. We give a characterization of the associate (resp., domainlike) pullback P of R1 → R3 ← R2 ,where R1 and R2 are two presimplifiable (resp., domainlike) rings. We prove that R is presimplifiable ring if and only if the factor ring R/nil(R)is presimplifiable and the ideal nil(R) is presimplifiable. Then we investigate the associate and presimplifiable property of the dual rings $R[x]/langle x^2 rangle$ and its modules through the base ring R and its modules.