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Krasner $F^{(m, n)}$-Hyperrings | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 5، دوره 11، شماره 6، اسفند 2014، صفحه 67-88 اصل مقاله (419.85 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1749 | ||
| نویسندگان | ||
B. Davvaz   ؛ M. Farshi
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| Department of Mathematics, Yazd University, Yazd, Iran | ||
| چکیده | ||
| $\!\!\!\!$ In this paper, the notion of fuzzy $\!$ Krasner $\!(m, n)$-hyperrings ($\!F^{(m, n)}\!$-hyperrings) by using the notion of $F^m$-hyperoperations and $F^n$-operations is introduced and some related properties are investigated. In this regards, relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner $(m, n)$-hyperrings are considered. We shall prove that every Krasner $F^{(m, n)}$-hyperring is extended by a Krasner $F^{(2, n)}$-hyperring. The concepts of normal $F$-hyperideals and homomorphisms of Krasner $F^{(m, n)}$-hyperrings are adopted. Also, the quotient of Krasner $F^{(m, n)}$-hyperrings by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Krasner $F^{(m, n)}$-hyperrings provided the $F$-hyperideals considered in them are normal. | ||
| کلیدواژه‌ها | ||
| Hyperstructure؛ Hyperoperation؛ $F^m$-hyperoperation؛ Krasner $(m؛ n)$-hyperring؛ Krasner $F^{(m؛ n)}$-hyperring؛ $F$-hyperideal؛ Regular and strongly regular relation | ||
| مراجع | ||
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