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 WNT2 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.
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