r-CLEAN RINGS RELATIVE TO RIGHT IDEALS | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 2، فروردین 2023، صفحه 203-224 اصل مقاله (170.72 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10627.1525 | ||
| نویسندگان | ||
| H. Ibrahim Hakmi* ؛ B. Ali Alussein | ||
| Department of Mathematics, Damascus University, Damascus, Syria. | ||
| چکیده | ||
| Abstract.An associative ring R with identity is called r¡clean ring 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 rings and r-clean rings of 2 2 matrices over R relative to some right ideal P. New characterization obtained include necessary and sufficient conditions of 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 ideal of it. | ||
| کلیدواژهها | ||
| (P-)idempotents؛ Regular and P-regular rings؛ clean and r-clean rings؛ r-clean ring relative to right ideal | ||
| مراجع | ||
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