%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 semihyper‌rings 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