r-clean rings relative to right ideals

An associative ring r with identity is called r-clean if every element of r is the sum of a regular and an idempotent element. in this paper, we introduce the concept of r- clean rings relative to right ideal. we study various properties of these rings. we give some relations between r-clean ring and r-clean ring of 22 matrices over r relative to some right ideal p. we give some necessary and sufficient conditions for a ring r to be r-clean, in terms of p-regular, p-local and p-clean properties of a given ring. also, we prove that every ring is r-clean relative to any maximal right ideal of it.