Applications of Hyperstructure Theory

Abstract

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A further study on ordered regular equivalence relations in ordered semihypergroups

“…Later on, people have observed that hyperstructures have many applications to several branches of both pure and applied sciences (see [2][3][4][5]). In particular, a semihypergroup is the simplest algebraic hyperstructure which possess the properties of closure and associativity.…”

“…In [23], Heidari and Davvaz applied the theory of hyperstructures to ordered semigroups and introduced the concept of ordered semihypergroups, which is a generalization of the concept of ordered semigroups. Also see [2]. The work on ordered semihypergroup theory can be found in [24][25][26][27].…”

Operations on hyperideals in ordered Krasner hyperrings

“…The hyperstructure theory and its applications have been investigated by the contribution of many mathematicians. The principal notions of hyperstructure theory can be found in [9,10,11,12,14,29].…”

Direct limit derived from twist product on G-semihypergroups

“…In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Since then, hundreds of papers and several books have been written on this topic, see [2][3][4].…”