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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| Format: | Article |
| Language: | English |
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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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| author | T. M. G. Ahsanullah Fawzi Al-Thukair |
| author_facet | T. M. G. Ahsanullah Fawzi Al-Thukair |
| author_sort | T. M. G. Ahsanullah |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-fdc81eea1fbf46578311599a4b5b6f75 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fdc81eea1fbf46578311599a4b5b6f752025-02-03T01:09:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041367969610.1155/S0161171204305247N-topo nilpotency in fuzzy neighborhood ringsT. M. G. Ahsanullah0Fawzi Al-Thukair1Department of Mathematics, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, King Saud University, Riyadh 11451, Saudi ArabiaWe 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.http://dx.doi.org/10.1155/S0161171204305247 |
| spellingShingle | T. M. G. Ahsanullah Fawzi Al-Thukair N-topo nilpotency in fuzzy neighborhood rings International Journal of Mathematics and Mathematical Sciences |
| title | N-topo nilpotency in fuzzy neighborhood rings |
| title_full | N-topo nilpotency in fuzzy neighborhood rings |
| title_fullStr | N-topo nilpotency in fuzzy neighborhood rings |
| title_full_unstemmed | N-topo nilpotency in fuzzy neighborhood rings |
| title_short | N-topo nilpotency in fuzzy neighborhood rings |
| title_sort | n topo nilpotency in fuzzy neighborhood rings |
| url | http://dx.doi.org/10.1155/S0161171204305247 |
| work_keys_str_mv | AT tmgahsanullah ntoponilpotencyinfuzzyneighborhoodrings AT fawzialthukair ntoponilpotencyinfuzzyneighborhoodrings |