N-topo nilpotency in fuzzy neighborhood rings

T. M. G. Ahsanullah and Fawzi Al-Thukair

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-18

Abstract:

We introduce the notion of N-topo nilpotent fuzzy set in a fuzzy neighborhood ring and develop some fundamental results. Here we show that a fuzzy neighborhood ring is locally inversely bounded if and only if for all 0 < α < 1 , the α -level topological rings are locally inversely bounded. This leads us to prove a characterization theorem which says that if a fuzzy neighborhood ring on a division ring is Wuyts-Lowen WNT 2 and locally inversely bounded, then the fuzzy neighborhood ring is a fuzzy neighborhood division ring. We also present another characterization theorem which says that a fuzzy neighborhood ring on a division ring is a fuzzy neighborhood division ring if the fuzzy neighborhood ring contains an N-topo nilpotent fuzzy neighborhood of zero.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:521581

DOI: 10.1155/S0161171204305247

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