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 $P-$local ($P-$regular) and local (regular) rings. New characterization obtained include necessary and sufficient conditions of a ring $R$ to be regular, local ring in terms $P-$regular, $P-$local of matrices ring $M_{2}(R)$. Also, We proved that every ring is local relative to any maximal right ideal of it.
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