NEW FUNDAMENTAL RELATIONS IN HYPERRINGS AND THE CORRESPONDING QUOTIENT STRUCTURES | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 21-41 اصل مقاله (193.26 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.10071.1501 | ||
| نویسندگان | ||
| Peyman Ghiasvand1؛ Saeed Mirvakili* 1؛ Bijan Davvaz2 | ||
| 1Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. | ||
| 2Department of Mathematical Sciences, Yazd University, Yazd, Iran. | ||
| چکیده | ||
| In this article, we introduce and analyze the smallest equivalence binary relation $\chi ^{*}$ on a hyperring $R$ such that the quotient $R/\chi ^{*}$, the set of all equivalence classes, is a commutative ring with identity and of characteristic $m$. The characterizations of commutative rings with identity via strongly regular relations is investigated and some properties on the topic are presented. Moreover, we introduce a new strongly regular relation $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring. Moreover, we introduce a new strongly regular relation $\sigma^{*}_{p}$ such that the quotient structure is a $p$-ring. | ||
| کلیدواژهها | ||
| Hyperring؛ fundamental relation؛ Strongly regular relation | ||
| مراجع | ||
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