پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 705 |
| تعداد مقالات | 10,146 |
| تعداد مشاهده مقاله | 71,451,118 |
| تعداد دریافت فایل اصل مقاله | 63,174,121 |
Weakly unit regular clean rings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 خرداد 1404 اصل مقاله (309.23 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 | ||
|
[1] M.S. Ahn and D.D. Anderson, Weakly clean rings and almost clean rings, Rocky Mount. J. Math. 36 (2006), 783–798. [2] D.D. Anderson and V.P. Camillo, Commutative rings whose elements are a sum of a unit and idempotent, Commun. Algebra, 30 (2002), no. 7, 3327–3336. [3] W.D. Burgess and R. Raphael, On embedding rings in clean rings, Commun. Algebra, 41 (2013), no. 2, 552–564. [4] V.P. Camillo and D. Khuran, A characterization of unit regular rings, Commun. Algebra, 29 (2001), no. 5, 2293–2295. [5] J. Chen and X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Commun. Algebra, 34 (2006), no. 10, 3659–3674. [6] A.Y.M. Chin and K.T. Qua, A note on weakly clean rings, Acta Math. Hungar. 132 (2011), no. 1–2, 113–116. [7] R. Gilmer and J. Huckaba, ∆-Rings, J. Algebra, 28 (1974), 414–432. [8] J. Han and W.K. Nicholson, Extensions of clean rings, Commun. Algebra, 29 (2001), 2589–2595. [9] H. Kambara, On directly finite regular rings, Osaka J. Math. 27 (1990), 629–654. [10] T. Kosan and S. Sahinkaya and Y. Zhou, On weakly clean rings, Comm. Algebra, 45 (2017), 8, 1–6. [11] J. Marot, Extension de la notion d’anneau valuation, Dept. Math. Faculté des Sci. Brest, 46 (1968), 39. [12] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977), 269–278. [13] W.K. Nicholson and Y. Zhou, Rings in which elements are uniquely the sum of an idempotent and a unit, Glasgow Math. J. 46 (2004), 227–236. [14] D. Portelli and W. Spangher, Krull rings with zero divisors, Comm. Algebra, 11 (1983), 1817–1851. [15] I.T. Younis and N.H. Shuker, Unit regular clean rings, J. Phys.: Conf. Ser. 1591 (2020), no. 1, 012049. [16] Y. Zhou and M. Ziembowski, On clean Laurent series rings, J. Aust. Math. Soc. 95 (2013), no. 3, 421–427. | ||
|
آمار تعداد مشاهده مقاله: 233 تعداد دریافت فایل اصل مقاله: 428 |
||