International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 473413, 9 pages
http://dx.doi.org/10.1155/2011/473413
Research Article

Two New Types of Rings Constructed from Quasiprime Ideals

Manal Ghanem1 and Hassan Al-Ezeh2

1Department of Mathematics, Irbid National University, Irbid 21110, Jordan
2Department of Mathematics, Jordan University, Amman 11942, Jordan

Received 23 October 2010; Accepted 16 March 2011

Academic Editor: Jianming Zhan

Copyright © 2011 Manal Ghanem and Hassan Al-Ezeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Keigher showed that quasi-prime ideals in differential commutative rings are analogues of prime ideals in commutative rings. In that direction, he introduced and studied new types of differential rings using quasi-prime ideals of a differential ring. In the same sprit, we define and study two new types of differential rings which lead to the mirrors of the corresponding results on von Neumann regular rings and principally flat rings (PF-rings) in commutative rings, especially, for rings of positive characteristic.