Paper Key : IRJ************399
Author: Jitendrasing Jaysing Patil
Date Published: 26 Oct 2023
Abstract
ABSTRACT :The properties of intra-regular -Semihyperring are studied. Also several characterizations of intra-regular -Semihyperring with the help of ideals, bi-ideals and quasi-ideals of -Semihyperrings has been done. INTRODUCTIONIn mathematics everyone is familiar to the classical algebraic structure in which composition of two elements is an element. But there is another view of mathematics in hyperstructure theory in which the composition of two element becomes a set. In 1934, the notion of hyperstructure was first introduced by French mathematician Marty when he presented a paper in conference. But still the theory of hyperstructure was not popular amongst the mathematicians in the word. After time passes it is found that the theory of hyperstructure has vast application in various branches of science and then theory of hyperstructure becomes popular and being studied by mathematicians across the word. In 2003, Corsini and Leoreanu 1 have given application of theory of hyperstructures in various subjects like: geometry, cryptography, artificial intelligence, relation algebras, automata, median algebras, relation algebras, fuzzy sets and codes. If we let H be a non-empty set. Then, the map oHHP^ (H) is called a hyperopertion, where P^ (H) is the family of all non-empty subsets of H and the couple (H,o) is called a hypergroupoid. Moreover, the couple (H,o) is called a semihypergroup if for every a,b,cH we have, (aob)o cao(boc). As theory of hyperstructure has vast application in various fields of sciences so it is essential to study the concepts of classical algebraic structure in hyperstructure theory. The main aim of this paper is to study the concepts of classical algebraic structure to a hyperstructure theory. In 3, Jagatap and Pawar introduced intra-regular -Semiring and made its characterizations with the help of ideals -Semirings. Here we have introduced the concept of intra-regular -Semihyperring and made its characterizations with the help of ideals, bi-ideals and quasi-ideals of -Semihyperrings analogues to Jagatap and Pawar 3.