P-Regular and P-Local Rings

This paper is a continuation of study rings relative to rightideal, where we study the concepts of regular and local ringsrelative to right ideal. We give some relations between P-local(P-regular) and local (regular) rings. New characterizationobtained include necessary and sufficient conditions of a ring Rto be regular, local ring in terms P-regular, P-local ofmatrices ring M_{۲}(R). Also, We proved that every ring is localrelative to any maximal right ideal of it.

Keywords:

P-idempotents , Regular and P-regular rings , Local and P-local rings , semi-potent rings