Prime and primary hyperideals in Krasner -hyperrings

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