  Let R be a Krasner (m,n)-hyperring and S be an n-ary multiplicative subset of
R. The purpose of this paper is to introduce the notion of n-ary S-prime
hyperideals as a new expansion of n-ary prime hyperideals. Several properties
and characterizations concerning n-ary S-prime hyperideals are presented. The
stability of this new concept with respect to various hyperring-theoretic
constructions are studied. Furthermore, we extend this concept to n-ary
S-primary hyperideals. We obtained some specific results explaining the
structure.
