%0 Journal Article
%T A Strong Regular Relation on ?-Semihyperrings
%J Journal of Sciences, Islamic Republic of Iran
%I University of Tehran
%Z 1016-1104
%A Davaz, B
%D 2011
%\ 09/01/2011
%V 22
%N 3
%P 257-266
%! A Strong Regular Relation on ?-Semihyperrings
%K Fundamental semiring
%K ?-semihyperring
%K ?-hyperring
%K Strongly regular relation
%R
%X The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyperâ€Œrings and a generalization of ?-semirings. In this paper, we introduce an equivalence relation ?* on a ?-semihyperrings R and we show that it is strongly regular. Furthermore, R/?*, the set of all equivalence classes of this relation is a ?/?*-semiring. The relation ?* is called the fundamental relation and the ?-semiring R/?* is called the fundamental semiring. Fundamental relations are the main tools in the study of ?-semihyperrings. We present some results about fundamental relations and fundamental semirings. Finally, we show that there is a covariant functor between the category of ?-semihyperrings and the category of semirings.
%U https://jsciences.ut.ac.ir/article_23588_7c25f0d0b9d6a7442490091706500b99.pdf