Topological conditions of NI near-rings
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In this paper we introduce the notion of NI near-rings similarto the notion introduced in rings. We give topological properties of col-lection of strongly prime ideals in NI near-rings. We have shown that ifN is a NI and weakly pm near-ring, then Max(N) is a compact Hausdorffspace. We have also shown that if N is a NI near-ring, then for everya a ∈ N, cl(D(a)) = V (N∗(N)a) = Supp(a) = SSpec(N)＼ int V (a).
Abstract
In this paper we introduce the notion of NI near-rings similarto the notion introduced in rings. We give topological properties of col-lection of strongly prime ideals in NI near-rings. We have shown that ifN is a NI and weakly pm near-ring, then Max(N) is a compact Hausdorffspace. We have also shown that if N is a NI near-ring, then for everya a ∈ N, cl(D(a)) = V (N∗(N)a) = Supp(a) = SSpec(N)＼ int V (a).
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