%0 Journal Article
%T r-CLEAN RINGS RELATIVE TO RIGHT IDEALS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Hakmi, H. Ibrahim
%A Alussein, B. Ali
%D 2023
%\ 01/01/2023
%V 10
%N 2
%P 203-224
%! r-CLEAN RINGS RELATIVE TO RIGHT IDEALS
%K (P-)idempotents
%K Regular and P-regular rings
%K clean and r-clean rings
%K r-clean ring relative to right ideal
%R 10.22044/jas.2021.10627.1525
%X Abstract.An associative ring R with identity is called r¡clean ring if everyelement 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 studyvarious properties of these rings. We give some relations between r-cleanrings and r-clean rings of 2 2 matrices over R relative to some right idealP. New characterization obtained include necessary and sufficient conditionsof a ring R to be r-clean in terms of P-regular, P-local and P-clean rings.Also, We prove that every ring is r-clean relative to any maximal right idealof it.
%U https://jas.shahroodut.ac.ir/article_2470_45b586cbdfdebd0f60d642784ff46ddd.pdf