We introduce the notion of multiendomorphism in a hypergroupoid and the notion of G-semiring. We show that, if (H, ∗) is a commutative semi-hypergroup, these multiendomorphisms form a G-semiring (E,+, ◦,≤), where the operation + is induced by ∗, ◦ is the usual composition of maps ◦ and ≤ is the usual inclusion of maps. Moreover, we show under which conditions the G-semiring (E,+, ◦,≤) is, in fa...

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d, C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the ...

A hypergroup is roughly speaking a locally compact Hausdorff space which has enough structure so that a convolution on the corresponding vector space of Radon measures makes it a Banach algebra. Hypergroups generalize in many ways topological groups. In this paper we extend to compact not necessarily commutative hypergroups some basic techniques on multipliers set forth for compact groups in He...

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. Q is permutably reducible ifQ(x1, . . . , xn) = P ` R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ́ where P and R are (n − k + 1)-ary and k-ary quasigroups, σ is a permutation, and 1 < k < n. An m-a...

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete or non-complete 1-hypergroups. Furthermore, classify the 1-hypergroups size 5 and 6 based on partition induced by fundamental relation ?. Many these can be obtained using aforesaid hypergroup construction.