On Weakly P.P. Rings

Abstract

We introduce, in this paper, the right weakly p.p. rings as the generalization of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.