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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 ![]() ![]() | ||
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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