n–ary hyperstructures constructed from binary quasi–ordered semigroups

Abstract

Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n-ary hyperstructures and binary relations we present a construction of n-ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.

Series of Semihypergroups of Time-Varying Artificial Neurons and Related Hyperstructures

“…In some constructions it is useful to apply the following lemma (called also the Ends-lemma having many applications-cf. [25][26][27][28][29]). Recall, first that by a (quasi-)ordered semigroup we mean a triad (S, ·, ≤), where (S, ·) is a semigroup, (S, ≤) is a (quasi-)ordered set, i.e., a set S endowed with a reflexive and transitive binary relation "≤" and for all triads of elements a, b, c ∈ S the implication…”

“…Concerning the basics of the hypergroup theory see also [23,[25][26][27][28][32][33][34][35][36][37][38][39][40][41].…”

“…Concerning the discussed theme see [26][27][28]30,32,36,39,45]. Now denote by S ⊆ C(T) an arbitrary non/empty subset and let P = {Ne( w u (t)); u ∈ S} ⊆ AN(T).…”

From lattices to Hv-matrices

“…Some of the hyperstructures are join spaces (not necessarily EL-join spaces) while others are EL-hypergroups which are not constructed from partially ordered groups. Properties of all these types of hyperstructures can be derived with the help of papers [12,20,21,22]. For a deeper insight in the properties of join spaces of the same type as (M m,n (S), ), see [6], chapter 4, or [17].…”

“…These had been constructed by a number of authors including Borzooei, et al, Chvalina, Davvaz, Dehghan Nezhad, Hošková and others [1,3,9,11] (see also book [8], sections 8.3 and 8.4.) before they were studied from the theoretical point of view [20,21,22].…”