| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,852,519 |
| تعداد دریافت فایل اصل مقاله | 9,586,536 |
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 | ||
| 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 | ||
|
\bibitem{book-corsini-1993} P. Corsini, {\it Prolegomena of hypergroup theory}, Aviani editore, Second edition, 1993. \bibitem{book-corsini-2003} P. Corsini and V. Leoreanu, {\it Applications of hyperstructures theory}, Advances in Mathematics, Kluwer Academic Publisher, 2003. \bibitem{Polygroup} B. Davvaz, {\em Polygroup theory and related systems}, World Scientific, 2013. \bibitem{k} B. Davvaz, {\it Fuzzy Krasner $(m,n)$-hyperrings}, Comput. Math. Appl., {\bf 59}\textbf{(12)} (2010), 3879-3891. \bibitem{davvaz-vougio-2006} B. Davvaz and T. Vougiouklis, {\it $n$-ary hypergroups}, Iran. J. Sci. Technol., Trans. A Sci., {\bf 30}\textbf{(2)} (2006), 165-174. \bibitem{davvaz1} B. Davvaz, {\it Isomorphism theorems of hyperrings}, Indian J. Pure Appl. Math., {\bf 35}\textbf{(3)} (2004), 321-331. \bibitem{dc} B. Davvaz and P. Corsini, {\it Fuzzy $n$-ary hypergroups}, J. Intell. Fuzzy Systems, {\bf 18}\textbf{(4)} (2007), 377-382. \bibitem{DDV} B. Davvaz, W. A. Dudek and T. Vougiouklis, {\it A generalization of $n$-ary algebraic systems}, Comm. Algebra, {\bf 37}\textbf{(4)} (2009), 1248-1263. \bibitem{krasner1} M. Krasner, {\it A class of hyperrings and hyperfields}, Internat. J. Math. Math. Sci., {\bf 6}\textbf{(2)} (1983), 307-312. \bibitem{krasner2} M. Krasner, {\it Approximation des corps values complets de caracteristque $p\neq0$ par ceux de caracteristique 0}, Actes due Colloque d' Algebre Superieure C.B.R.M, Bruxelles, (1965), 12-22. \bibitem{leoreanu-davvaz} V.~Leoreanu-Fotea and B.~Davvaz, {\em $n$-hypergroups and binary relations}, European J. Combin., {\bf 29}\textbf{(5)} (2008), 1207-1218. \bibitem{mirvakili-krasner} S. Mirvakili and B. Davvaz, {\it Relations on krasner $(m, n)$-hyperrings}, European J. Combin., {\bf 31}\textbf{(3)} (2010), 790-802. \bibitem{rosenfeld1} A.~Rosenfeld, {\it Fuzzy groups}, J. Math. Anal. Appl., {\bf 35} (1971), 512-517. \bibitem{V} T. Vougiouklis, {\it Hyperstructures and their representations}, Hadronic Press, Inc, 115, Palm Harber, USA, 1994. \bibitem{zadeh} L.~A. Zadeh, {\it Fuzzy sets}, Information and Control, {\bf 8} (1965), 338-353. \bibitem{zahedi2} M. M. Zahedi and A. Hasankhani, {\it F-polygroups {I}}, J. Fuzzy Math., {\bf 4}\textbf{(3)} (1996), 533-548. \bibitem{zahedi3} M. M. Zahedi and A. Hasankhani, {\it F-polygroups {II}}, Information Sciences, {\bf 89}\textbf{(3-4)} (1996), 225-243. | ||
|
آمار تعداد مشاهده مقاله: 2,341 تعداد دریافت فایل اصل مقاله: 1,459 |
||