Some properties of Associate and Presimplifiable rings

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]/(x2) and its modules through the base ring R and its modules.