Krasner $F^{(m, n)}$-Hyperrings

Document Type: Research Paper


Department of Mathematics, Yazd University, Yazd, Iran


$\!\!\!\!$ 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.


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