{"id":"https://openalex.org/W2281582997","doi":"https://doi.org/10.1515/forma-2015-0011","title":"Finite Product of Semiring of Sets","display_name":"Finite Product of Semiring of Sets","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W2281582997","doi":"https://doi.org/10.1515/forma-2015-0011","mag":"2281582997"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2015-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/23/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://content.sciendo.com/downloadpdf/journals/forma/23/2/article-p107.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068514239","display_name":"Roland Coghetto","orcid":"https://orcid.org/0000-0002-4901-0766"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roland Coghetto","raw_affiliation_strings":["Rue de la Brasserie 5 7100 La Louvi\u00e8re, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rue de la Brasserie 5 7100 La Louvi\u00e8re, Belgium","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068514239"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16630281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"2","first_page":"107","last_page":"114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9445000290870667,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9445000290870667,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9354000091552734,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9124000072479248,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiring","display_name":"Semiring","score":0.9862009286880493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7966256141662598},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7751109600067139},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5404714941978455},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4598601162433624},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45474693179130554},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43142884969711304},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35717809200286865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33843064308166504},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11005759239196777}],"concepts":[{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.9862009286880493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7966256141662598},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7751109600067139},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5404714941978455},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4598601162433624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45474693179130554},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43142884969711304},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35717809200286865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33843064308166504},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11005759239196777},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2015-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/23/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:28e9089173184a03a88e8ad646fabd57","is_oa":false,"landing_page_url":"https://doaj.org/article/28e9089173184a03a88e8ad646fabd57","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 23, Iss 2, Pp 107-114 (2015)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/4875","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/4875","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"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"}],"best_oa_location":{"id":"doi:10.1515/forma-2015-0011","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2015-0011","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/23/2/article-p107.pdf","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2281582997.pdf","grobid_xml":"https://content.openalex.org/works/W2281582997.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W177314244","https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W1029783734","https://openalex.org/W1176327680","https://openalex.org/W1539396145","https://openalex.org/W2099252149","https://openalex.org/W2104238184","https://openalex.org/W2105559527","https://openalex.org/W2148145049","https://openalex.org/W2150348213","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W3203406682","https://openalex.org/W4285719527","https://openalex.org/W4310300362"],"related_works":["https://openalex.org/W185248416","https://openalex.org/W4312619976","https://openalex.org/W202649520","https://openalex.org/W2381312783","https://openalex.org/W2186303141","https://openalex.org/W2371578151","https://openalex.org/W2057864982","https://openalex.org/W4312720755","https://openalex.org/W2183214273","https://openalex.org/W2351097202"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"formalize":[2],"that":[3,38,55],"the":[4,39,56,78,81],"image":[5],"of":[6,9,19,25,28,42,45,51,59,63,70,83],"a":[7,17,22,26,31,43,49,60,67],"semiring":[8,18,27,44,50,62,69],"sets":[10,29,46,52,64],"[17]":[11],"by":[12],"an":[13],"injective":[14],"function":[15],"is":[16,47,66],"sets.We":[20],"offer":[21],"non-trivial":[23],"example":[24],"in":[30],"topological":[32],"space":[33],"[21].":[34],"Finally,":[35],"we":[36,75],"show":[37],"finite":[40,57],"product":[41,58],"also":[48],"[21]":[53],"and":[54,85],"classical":[61,68],"[8]":[65],"sets.":[71],"In":[72],"this":[73],"case,":[74],"use":[76],"here":[77],"notation":[79],"from":[80],"book":[82],"Aliprantis":[84],"Border":[86],"[1].":[87]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
