Krasner $F^{(m, n)}$-Hyperrings
نویسندگان
1 Department of Mathematics, Yazd University, Yazd, Iran
2 Department of Mathematics, Yazd University, Yazd, Iran.
doi
10.22111/ijfs.2014.1749چکیده
$\!\!\!\!$ 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 somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperring is extended by a Krasner $F^{(2,n)}$-hyperring. The concepts of normal $F$-hyperideals andhomomorphisms of Krasner $F^{(m, n)}$-hyperrings are adopted.Also, the quotient of Krasner $F^{(m, n)}$-hyperrings by definingregular relations are studied. Finally, the classical isomorphismtheorems of groups are generalized to Krasner $F^{(m,n)}$-hyperrings provided the $F$-hyperideals considered in themare normal.
