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Weakly unit regular clean rings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 17، شماره 6، شهریور 2026، صفحه 153-157 اصل مقاله (305.92 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33551.5004 | ||
| نویسنده | ||
| Fatemeh Rashedi* | ||
| Department of Mathematics, Technical and Vocational University (TVU), Tehran, Iran | ||
| تاریخ دریافت: 26 اسفند 1402، تاریخ پذیرش: 15 اردیبهشت 1403 | ||
| چکیده | ||
| A ring $R$ is called clean if every member of $R$ is the sum of a self-resolved member and an invertible member. Also, we call the ring $R$ weakly clean if every member of $R$ can be written as the sum or difference of an invertible member and an autoregressive member. The $a\in R$ member is called unit regular whenever $u\in U(R)$ exists such $a=aua$. A ring $R$ is called a clean unit if every member of $R$ is the sum of an autonomial member and a unitary member. We call a ring $R$ a weakly clean unit if every member of $R$ can be written as the sum or difference of a unit regular and a self-power term. In this paper, weakly unit regular clean rings are introduced and discussed. In particular, we show that if $\{R_i\}_{i\in I}$ is a family of commutative rings, then $R=\prod_{i\in I} R_i$ is weakly unit regular clean if and only if every $R_i$ is weakly clean regular unit and at most one $R_i$'s are not clean and regular units. | ||
| کلیدواژهها | ||
| clean rings؛ weakly clean rings؛ unit clean rings؛ weakly clean regular rings | ||
| مراجع | ||
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