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Some characterizations of the maximal ZG-regular ideal in a ring | ||
| Journal of Hyperstructures | ||
| دوره 14، شماره 2، اسفند 2025، صفحه 176-183 اصل مقاله (1.6 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.17344.1090 | ||
| نویسنده | ||
| Marzieh Farmani* | ||
| Department of Mathematices, Islamic Azad University, Roudehen Branch, Roudehen, Tehran, Iran. | ||
| چکیده | ||
| Let R be an associative ring with identity. A ring R is called ZG-regular( resp. strongly ZG-regular) if, for every a in R, there exist positive integer n and g in G, such that ang ∈a^ngRa^ng (resp. a^ng ∈a^(n+1)gR. In this paper, we shall show that the join of all ZG-regular ideals in an arbitrary ring R is a ZG-regular ideal, and so there exists a unique maximal ZG-regular ideal M = M(R) in R, whose structure we investigate. Furthermore, we establish the necessary and sufficient condition for a ring to be a direct sum of its ideals. | ||
| کلیدواژهها | ||
| group؛ ring؛ ZG-regular؛ strongly ZG-regular؛ maximal ZG-regular ideal | ||
| مراجع | ||
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