Relationship between Rings and Hyperrings by Using the Notion of Fundamental Relations

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. The fundamental relation α on hyperrings is studied by Davvaz and Vougiouklis in Communications in Algebra 8 Davvaz , B. , Vougiouklis , T. ( 2007 ). Commutative rings obtained from hyperrings (H _v -rings) with α*-relations . Comm. Algebra 35 ( 11 ): 3307 – 3320 .Taylor &; Francis Online], Web of Science ®] , Google Scholar]]. Now, in this article, we obtain more results about this relation. In particular, we determine necessary and sufficient conditions such that the relation α is transitive.