N-topo nilpotency in fuzzy neighborhood rings
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 lead...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204305247 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |