3-r-hyperideals and 0-3-r-hyperideals of commutative Krasner hyperrings

This paper deals with an important class of multialgebras, called Krasner hyperrings. Our purpose is to define the expansion of r-hyperideals and to extend this concept to 0-3-r-hyperideal in commutative Krasner hyperrings with nonzero identity. 3-r-hyperideals of commutative Krasner hyperrings are studied. Some properties of 0 -3-r-hyperideals are investigated and several examples are provided.