Topological conditions of NI near-rings
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 669-677
Printed October 1, 2013
P. Dheena and C. Jenila
Annamalai University, Annamalai University
Abstract : In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if $N$ is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if $N$ is a NI near-ring, then for every $a\in N,$ $cl(D(a))=V(N^{*}(N)_{a})=Supp(a)=SSpec(N)\backslash int~ V(a).$
Keywords : NI near-ring, strongly prime ideal, weakly pm near-ring, symmetric near-ring
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