{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T20:40:02Z","timestamp":1723063202186},"reference-count":0,"publisher":"Wiley","issue":"13","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"KSU Research Center","award":["1423\/07"],"award-info":[{"award-number":["1423\/07"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>We introduce the notion of N\u2010topo 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 &lt; <jats:italic>\u03b1<\/jats:italic> &lt; 1, the <jats:italic>\u03b1<\/jats:italic>\u2010level 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\u2010Lowen WNT<jats:sub><jats:italic>2<\/jats:italic><\/jats:sub> 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\u2010topo nilpotent fuzzy neighborhood of zero.<\/jats:p>","DOI":"10.1155\/s0161171204305247","type":"journal-article","created":{"date-parts":[[2004,6,24]],"date-time":"2004-06-24T17:59:33Z","timestamp":1088099973000},"page":"679-696","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["N\u2010topo nilpotency in fuzzy neighborhood rings"],"prefix":"10.1155","volume":"2004","author":[{"given":"T. M. G.","family":"Ahsanullah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fawzi","family":"Al-Thukair","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,3,23]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/521581.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204305247","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T19:40:14Z","timestamp":1723059614000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204305247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204305247"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204305247","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2003-05-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-03-23","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}