Prime and primary hyperideals in Krasner (m,n)(m,n)-hyperrings

We introduce and study the quotient structure and an nn-ary hyperintegral domain of a Krasner (m,n)(m,n)-hyperring, proving some results regarding them. Also, we introduce some important hyperideals such as Jacobson radical, nn-ary prime and primary hyperideals, nilradical, and nn-ary multiplicative subsets of Krasner (m,n)(m,n)-hyperrings. Finally we investigate the links between these notions.