Applications of the α⁎-relation to Krasner hyperrings

This paper deals with a special type of hyperrings called Krasner hyperring. The main tool is the studding of the α⁎-relation. The α⁎-relation was introduced by Davvaz and Vougiouklis. Indeed, we use the α⁎-relation in a given Krasner hyperring. In this way, the α⁎-relation is the smallest equivalence relation on a Krasner hyperring R such that R/α⁎ is a commutative ring. Results are obtained on Krasner hyperrings, derived hyperrings and α-parts.