Hyper ideals on Zariski topology in hyper vector space

In this study, the set of all prime hyperideals in the commutative hyperring R is shown with Spec(R). A relation is found between the open sets X_J and the hyperideals J of the Zariski topology constructed on Spec(R). Hypercompositional characterizations are obtained using basic topological properties. The characterizations of semicompact, dense, irreducible subsets of each open subset of the Zariski topology are made with the help of Noether spectrum. n-hyperideals are defined in commutative Krasner hyperrings. Algebraic properties of n-hyperideals are given. By generalizing this concept, S-n-hyperideals have been defined in commutative Krasner hyperrings. Prime hyperideals are generalized to S-n-hyperideals and thus the S-n-Zariski topology Spec∗, which is ageneralization of the Zariski topology Spec, is classified with the help of S-n-hyperideals. Also, the basis of S-n-Zariski subhypervector space, which is defined as the generalization of Zariski subhypervector space, is found.