The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

we study harmonic analysis on cocommutative kpc-hyper-groups‎, which is a generalization of djs-hypergroups‎, ‎introduced by kalyuzhnyi‎, ‎podkolzin and chapovsky‎. ‎we prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a radon measure on kpc-hypergroup $q$ and $gamma$ is a character on $q$.

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

We study harmonic analysis on cocommutative KPC-hyper-groups‎, which is a generalization of DJS-hypergroups‎, ‎introduced by Kalyuzhnyi‎, ‎Podkolzin and Chapovsky‎. ‎We prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a Radon measure on KPC-hypergroup $Q$ and $gamma$ is a character on $Q$.

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...

Group recommendation aims to recommend items a group of users. In this work, we study in particular scenario, namely occasional recommendation, where groups are formed ad hoc and users may just constitute for the first time—that is, historical group-item interaction records highly limited. Most state-of-the-art works have addressed challenge by aggregating members’ personal preferences learn re...

the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary...