r -Hyperideals and Generalizations of r -Hyperideals in Krasner Hyperrings

Abstract

This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r -hyperideals in commutative Krasner hyperrings. Some properties of p r -hyperideals are also studied. The relation between prime hyperideals and r -hyperideals is investigated. We show that the image and the inverse image of an r -hyperideal are also an r -hyperideal. We also introduce a generalization of r -hyperideals, and we prove some properties of them.