{"id":"https://openalex.org/W2145939341","doi":"https://doi.org/10.1155/s0161171204311130","title":"Weak incidence algebra and maximal ring of quotients","display_name":"Weak incidence algebra and maximal ring of quotients","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2145939341","doi":"https://doi.org/10.1155/s0161171204311130","mag":"2145939341"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204311130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204311130","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/846181.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/2004/846181.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045105273","display_name":"Surjeet Singh","orcid":"https://orcid.org/0000-0002-4646-2089"},"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":"Surjeet Singh","raw_affiliation_strings":["Department of Mathematics, King Saud University, PO Box 2455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, PO Box 2455","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, PO Box 2455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, King Saud University, PO Box 2455","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":0.5958,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6796875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2004","issue":"53","first_page":"2835","last_page":"2845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7909191846847534},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.7139010429382324},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6088468432426453},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5434536933898926},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.52961266040802},{"id":"https://openalex.org/keywords/incidence-algebra","display_name":"Incidence algebra","score":0.5263838768005371},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.47951915860176086},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4171958863735199},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.41125842928886414},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31791388988494873},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2934207022190094},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21437078714370728},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.13578155636787415},{"id":"https://openalex.org/keywords/filtered-algebra","display_name":"Filtered algebra","score":0.1271790862083435}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7909191846847534},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.7139010429382324},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6088468432426453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5434536933898926},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.52961266040802},{"id":"https://openalex.org/C115179944","wikidata":"https://www.wikidata.org/wiki/Q371133","display_name":"Incidence algebra","level":5,"score":0.5263838768005371},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.47951915860176086},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4171958863735199},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.41125842928886414},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31791388988494873},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2934207022190094},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21437078714370728},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.13578155636787415},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.1271790862083435},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/s0161171204311130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204311130","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/846181.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:846181","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/846181.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:1940616d400745b787ebc2d82f0ce9d9","is_oa":true,"landing_page_url":"https://doaj.org/article/1940616d400745b787ebc2d82f0ce9d9","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 53, Pp 2835-2845 (2004)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/S0161171204311130","is_oa":false,"landing_page_url":"https://doi.org/10.1155/S0161171204311130","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1155/s0161171204311130","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204311130","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2004/846181.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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2145939341.pdf","grobid_xml":"https://content.openalex.org/works/W2145939341.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W95008133","https://openalex.org/W1538620891","https://openalex.org/W1579739595","https://openalex.org/W1595020125","https://openalex.org/W1609166329","https://openalex.org/W1998116779","https://openalex.org/W2100464946","https://openalex.org/W2161396108","https://openalex.org/W2168927172","https://openalex.org/W4206738103","https://openalex.org/W6637839640","https://openalex.org/W6814944288"],"related_works":["https://openalex.org/W4308298797","https://openalex.org/W2030374326","https://openalex.org/W4255963200","https://openalex.org/W2360590989","https://openalex.org/W2369074270","https://openalex.org/W4255391830","https://openalex.org/W2015466415","https://openalex.org/W2953844587","https://openalex.org/W4288363881","https://openalex.org/W1565509971"],"abstract_inverted_index":{"Let":[0],"X":[1,3,24,32,45,52,60,62,74,100,114,116,170,193,269,282,301,306,319,337],",":[2,25,33,46,54,101,124,143,154,164,171,177,182,185,194,212,219,226,239,245,252,261,270,302,320,338],"\u2032":[4,53,63],"be":[5,14,78,105,365],"two":[6],"locally":[7,79],"finite,":[8],"preordered":[9,72],"sets":[10],"and":[11,49,61,133,150,186,325],"let":[12],"R":[13,26,47,55,102,118,172,176,195,271,274,284,303,321,339],"any":[15,162],"indecomposable":[16],"commutative":[17],"ring.":[18],"The":[19],"incidence":[20,279],"algebra":[21,280],"I":[22,43,50,97,167,190,266,298,316,334],"(":[23,44,51,99,122,141,152,169,192,199,210,217,224,237,243,250,259,268,300,318,336],"),":[27,173,221,247],"in":[28,189],"a":[29,71,352],"sense,":[30],"represents":[31,305],"because":[34],"of":[35,87,91,108,138,281,290,315,331,333,355,361,372],"the":[36,41,83,106,134,277,287,291,311,326,347],"well\u2010known":[37],"result":[38],"that":[39,75,85,120,198,296,346],"if":[40],"rings":[42,356],")":[48,56,103,126,145,156,196,207,214,228,241,254,272,304,322,340],"are":[57,64,323],"isomorphic,":[58],"then":[59],"isomorphic.":[65],"In":[66,286],"this":[67,309],"paper,":[68],"we":[69],"consider":[70],"set":[73,107,135],"need":[76,363],"not":[77,364],"finite":[80],"but":[81],"has":[82],"property":[84],"each":[86],"its":[88,368],"equivalence":[89],"classes":[90],"equivalent":[92],"elements":[93],"is":[94,159,294,341,344],"finite.":[95,160],"Define":[96],"*":[98,168,191,267,299,317,335],"to":[104,367],"all":[109,310],"those":[110],"functions":[111],"f":[112,121,137,151,163,179,183,188,200,209,222,236,249,258],":":[113],"\u00d7":[115],"\u2192":[117],"such":[119,197],"x":[123,130,142,147,153,204,211,218,225,231,238,251,260],"y":[125,132,144,149,155,206,213,220,227,235,246,253,262],"=":[127,208,229,255],"0,":[128],"whenever":[129],"\u2a7d":[131],"S":[136],"ordered":[139],"pairs":[140],"with":[146],"<":[148],"\u2260":[157],"0":[158],"For":[161],"g":[165,181,184,202,216,223,242],"\u2208":[166,175],"r":[174,187,248,256],"define":[178],"+":[180,201,205,215],")(":[203],"\u2211":[230],"\u2264":[232,234],"z":[233,240,244],"\u00b7":[257],").":[263],"This":[264],"makes":[265],"an":[273],"\u2010algebra,":[275],"called":[276],"weak":[278],"over":[283],".":[285,307],"first":[288],"part":[289],"paper":[292],"it":[293],"shown":[295,345],"indeed":[297],"After":[308],"essential":[312],"one\u2010sided":[313],"ideals":[314],"determined":[324],"maximal":[327,358,369],"right":[328,359],"(left)":[329],"ring":[330,360,371],"quotients":[332,362],"discussed.":[342],"It":[343],"results":[348],"proved":[349],"can":[350],"give":[351],"large":[353],"class":[354],"whose":[357],"isomorphic":[366],"left":[370],"quotients.":[373]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}