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N-topo nilpotency in fuzzy neighborhood rings

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

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.

Suggested Citation

  • T. M. G. Ahsanullah & Fawzi Al-Thukair, 2004. "N-topo nilpotency in fuzzy neighborhood rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-18, January.
    • Handle: RePEc:hin:jijmms:521581
    DOI: 10.1155/S0161171204305247
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