پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 861 |
| تعداد مقالات | 8,370 |
| تعداد مشاهده مقاله | 53,157,189 |
| تعداد دریافت فایل اصل مقاله | 9,418,253 |
Ring in which every element is sum of two 6-potent elements | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403 اصل مقاله (157.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26096.1605 | ||
| نویسندگان | ||
| K. N. Deka* ؛ H. K. Saikia | ||
| Department of Mathematics, Gauhati University, Guwahati, India | ||
| چکیده | ||
| In this paper, we prove the following results. Every element of a ring $R$ is a sum of two commuting $6-$potent elements if and only if $R$ is isomorphic to $R_1\times R_2\times R_3$, where $R_1$ is isomorphic to a subdirect product of $Z_2$'s, $R_2$ is isomorphic to a subdirect product of $Z_3$'s and $R_3$ is isomorphic to a subdirect product of $Z_{11}$'s. Also, if every element of a ring $R$ is the sum of two 6-potent and one nilpotent all commute with each other, then $R$ is isomorphic to $R_1\times R_2\times R_3$, where $J(R_1)$ is nil and $R_1/J(R_1)$ is a subdirect product of rings isomorphic to either of the rings $Z_2,F_4,M_2(F_2)$ and $M_2(F_4)$ , $a^{81}-a$ is nilpotent for every $a\in R_2$ , $J(R_3)$ is nil and $R_3/J(R_3)$ is a subdirect product of $Z_{11}$'s. | ||
| کلیدواژهها | ||
| 4-potents؛ 6-potents؛ Chinese Remainder Theorem | ||
|
آمار تعداد مشاهده مقاله: 418 تعداد دریافت فایل اصل مقاله: 12 |
||