Some properties of Associate and Presimplifiable rings

Authors

MANAL GHANEM

DOI

10.3906/mat-0909-14

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 R_1 \rightarrow{R_3} \leftarrow{R_2}, where R_1 and R_2 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.

Keywords

Associate ring, presimplifiable ring, domainlike, pullback and dual ring

First Page

333

Last Page

340

Recommended Citation

GHANEM, MANAL (2011) "Some properties of Associate and Presimplifiable rings," Turkish Journal of Mathematics: Vol. 35: No. 2, Article 14. https://doi.org/10.3906/mat-0909-14
Available at: https://journals.tubitak.gov.tr/math/vol35/iss2/14