In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in algebra will be endo-linearly represented over the same binary group. Schauffler like theorem proved for those algebras.

This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion (softly) left regularity, right intra-regularity, complete generalized regularity investigate their related properties. Several characterizations them in terms provided. Finally, relationships betwee...

This paper investigates the question of when a finite hypergroup with three elements is strong, that is satisfies the condition that its dual signed hypergroup is actually a hypergroup. We classify hermitian hypergroups of order three by weight into two dimensional families and show that the algebraic conditions arising from duality yield four interesting curves in the plane which bound the cha...

Percolation theory is a subject that has been flourishing in recent decades. Because of its simple expression and rich connotation, it widely used chemistry, ecology, physics, materials science, infectious diseases, complex networks. Consider an infinite-rooted N-ary tree where each vertex assigned i.i.d. random variable. When the variable follows Bernoulli distribution, path called head run if...

A homomorphism of a hypergroup (H, ◦) is a function f : H → H satisfying f(x ◦ y) ⊆ f(x) ◦ f(y) for all x, y ∈ H. A homomorphism of a hypergroup (H, ◦) is called an epimorphism if f(H) = H. Denote by Hom(H, ◦) and Epi(H, ◦) the set of all homomorphisms and the set of all epimorphisms of a hypergroup (H, ◦), respectively. In this paper, the elements of Hom(Zn, ◦m) and Epi(Zn, ◦m) are characteriz...

Conformal inclusions of chiral conformal field theories, or more generally quantum are described in the von Neumann algebraic setting by nets subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation mind, we study a purely subfactor theoretical context certain class braided discrete subfactors an additional commutativity constraint, tha...