{"id":"https://openalex.org/W2165287185","doi":"https://doi.org/10.1155/s0161171204305247","title":"N\u2010topo nilpotency in fuzzy neighborhood rings","display_name":"N\u2010topo nilpotency in fuzzy neighborhood rings","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2165287185","doi":"https://doi.org/10.1155/s0161171204305247","mag":"2165287185"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204305247","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204305247","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/521581.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2004/521581.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010778664","display_name":"T. M. G. Ahsanullah","orcid":"https://orcid.org/0000-0002-3012-566X"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"T. M. G. Ahsanullah","raw_affiliation_strings":["Department of Mathematics, King Saud University, Riyadh 11451"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, Riyadh 11451","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058850226","display_name":"Fawzi Al-Thukair","orcid":"https://orcid.org/0000-0003-1126-010X"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fawzi Al-Thukair","raw_affiliation_strings":["Department of Mathematics, King Saud University, Riyadh 11451"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, Riyadh 11451","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21417654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2004","issue":"13","first_page":"679","last_page":"696"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9793000221252441,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8864628076553345},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6699782609939575},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.6383763551712036},{"id":"https://openalex.org/keywords/division-ring","display_name":"Division ring","score":0.6317065954208374},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.6230472326278687},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6077061295509338},{"id":"https://openalex.org/keywords/locally-nilpotent","display_name":"Locally nilpotent","score":0.5508402585983276},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4973616898059845},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4885352551937103},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41004669666290283},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.32406556606292725},{"id":"https://openalex.org/keywords/nilpotent-group","display_name":"Nilpotent group","score":0.1740511953830719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14549008011817932},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08133649826049805},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07200783491134644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0561755895614624}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8864628076553345},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6699782609939575},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6383763551712036},{"id":"https://openalex.org/C31671303","wikidata":"https://www.wikidata.org/wiki/Q650741","display_name":"Division ring","level":3,"score":0.6317065954208374},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.6230472326278687},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6077061295509338},{"id":"https://openalex.org/C2776456406","wikidata":"https://www.wikidata.org/wiki/Q6664692","display_name":"Locally nilpotent","level":4,"score":0.5508402585983276},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4973616898059845},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4885352551937103},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41004669666290283},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.32406556606292725},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.1740511953830719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14549008011817932},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08133649826049805},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07200783491134644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0561755895614624},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/s0161171204305247","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204305247","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/521581.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:521581","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/521581.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:fdc81eea1fbf46578311599a4b5b6f75","is_oa":true,"landing_page_url":"https://doaj.org/article/fdc81eea1fbf46578311599a4b5b6f75","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 13, Pp 679-696 (2004)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/s0161171204305247","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204305247","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/521581.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.49000000953674316}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2165287185.pdf","grobid_xml":"https://content.openalex.org/works/W2165287185.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1964056265","https://openalex.org/W1975192283","https://openalex.org/W1978339398","https://openalex.org/W1980566588","https://openalex.org/W1990351279","https://openalex.org/W2006176153","https://openalex.org/W2036104856","https://openalex.org/W2056664771","https://openalex.org/W2060684448","https://openalex.org/W2088252380","https://openalex.org/W2090032238","https://openalex.org/W2153689313","https://openalex.org/W2169518916","https://openalex.org/W6600424091","https://openalex.org/W6600493712","https://openalex.org/W6604883494","https://openalex.org/W6674356575"],"related_works":["https://openalex.org/W2022472189","https://openalex.org/W4294168466","https://openalex.org/W2379498264","https://openalex.org/W4223469647","https://openalex.org/W1565833102","https://openalex.org/W2264352149","https://openalex.org/W4229596634","https://openalex.org/W4300430055","https://openalex.org/W2963861343","https://openalex.org/W3042921979"],"abstract_inverted_index":{"We":[0,90],"introduce":[1],"the":[2,42,80,114],"notion":[3],"of":[4,124],"N\u2010topo":[5,120],"nilpotent":[6,121],"fuzzy":[7,11,24,64,81,86,100,109,115,122],"set":[8],"in":[9],"a":[10,23,56,63,68,85,99,104,108],"neighborhood":[12,25,65,82,87,101,110,116,123],"ring":[13,26,66,70,83,102,106,112,117],"and":[14,32,75],"develop":[15],"some":[16],"fundamental":[17],"results.":[18],"Here":[19],"we":[20],"show":[21],"that":[22,61,98],"is":[27,71,84,107],"locally":[28,48,76],"inversely":[29,49,77],"bounded":[30],"if":[31,34,62,113],"only":[33],"for":[35],"all":[36],"0":[37],"<":[38,40],"\u03b1":[39,43],"1,":[41],"\u2010level":[44],"topological":[45],"rings":[46],"are":[47],"bounded.":[50],"This":[51],"leads":[52],"us":[53],"to":[54],"prove":[55],"characterization":[57,94],"theorem":[58,95],"which":[59,96],"says":[60,97],"on":[67,103],"division":[69,88,105,111],"Wuyts\u2010Lowen":[72],"WNT":[73],"2":[74],"bounded,":[78],"then":[79],"ring.":[89],"also":[91],"present":[92],"another":[93],"contains":[118],"an":[119],"zero.":[125]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}