P-Regular and P-Local Rings

Document Type : Research Paper

Author

Department of Mathematics Faculty of Sciences Damascus University, Syria

Abstract

This paper is a continuation of study rings relative to right
ideal, where we study the concepts of regular and local rings
relative to right ideal. We give some relations between Plocal
(Pregular) and local (regular) rings. New characterization
obtained include necessary and sufficient conditions of a ring R
to be regular, local ring in terms Pregular, Plocal of
matrices ring M2(R). Also, We proved that every ring is local
relative to any maximal right ideal of it.

Keywords