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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 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26096.1605 | ||
| نویسندگان | ||
| K. N. Deka* 1؛ H. K. Saikia2 | ||
| 1Dept of Mathematics, Gauhati University | ||
| 2Dept. of Mathematics, Gauhati University, Guwahati-781014, Assam, 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×R_2×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 sum of two 6-potent and one nilpotent all commute each other then R is isomorphic to R_1×R_2×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 R2 , 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 | ||
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آمار تعداد مشاهده مقاله: 94 |
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