{"id":"https://openalex.org/W2614270863","doi":"https://doi.org/10.1515/forma-2017-0006","title":"Ordered Rings and Fields","display_name":"Ordered Rings and Fields","publication_year":2017,"publication_date":"2017-03-28","ids":{"openalex":"https://openalex.org/W2614270863","doi":"https://doi.org/10.1515/forma-2017-0006","mag":"2614270863"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2017-0006","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0006","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/1/article-p63.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/25/1/article-p63.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048465549","display_name":"Christoph Schwarzweller","orcid":"https://orcid.org/0000-0001-9587-8737"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Christoph Schwarzweller","raw_affiliation_strings":["Institute of Informatics, University of Gdansk , Gdansk , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Gdansk , Gdansk , Poland","institution_ids":["https://openalex.org/I40413290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048465549"],"corresponding_institution_ids":["https://openalex.org/I40413290"],"apc_list":null,"apc_paid":null,"fwci":0.5858,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60989746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"1","first_page":"63","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9991999864578247,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9991999864578247,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9980999827384949,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8689004182815552},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6397097110748291},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5976613163948059},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5551015138626099},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.5342943072319031},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5311499834060669},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4429212212562561},{"id":"https://openalex.org/keywords/ordered-field","display_name":"Ordered field","score":0.41173046827316284},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40365755558013916},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4004349708557129},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34918588399887085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.093523770570755},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08006256818771362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8689004182815552},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6397097110748291},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5976613163948059},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5551015138626099},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.5342943072319031},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5311499834060669},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4429212212562561},{"id":"https://openalex.org/C13851312","wikidata":"https://www.wikidata.org/wiki/Q909412","display_name":"Ordered field","level":2,"score":0.41173046827316284},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40365755558013916},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4004349708557129},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34918588399887085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.093523770570755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08006256818771362},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/forma-2017-0006","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0006","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/1/article-p63.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:repozytorium.uwb.edu.pl:11320/5570","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/5570","pdf_url":"http://hdl.handle.net/11320/5570","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"},{"id":"pmh:oai:doaj.org/article:13560b0d3e2c4e34b2930e2ff9a693f0","is_oa":false,"landing_page_url":"https://doaj.org/article/13560b0d3e2c4e34b2930e2ff9a693f0","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 25, Iss 1, Pp 63-72 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/forma-2017-0006","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2017-0006","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/25/1/article-p63.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/W2614270863.pdf","grobid_xml":"https://content.openalex.org/works/W2614270863.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1553126454","https://openalex.org/W2057691643","https://openalex.org/W2105559527","https://openalex.org/W2138253682","https://openalex.org/W2147599721","https://openalex.org/W2184838578","https://openalex.org/W2526342011"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4248087735","https://openalex.org/W4225310406","https://openalex.org/W4229560034","https://openalex.org/W1542828544","https://openalex.org/W2750830833"],"abstract_inverted_index":{"Summary":[0],"We":[1,13],"introduce":[2],"ordered":[3,27,43],"rings":[4,31,40],"and":[5,23,32],"fields":[6],"following":[7],"Artin-Schreier\u2019s":[8],"approach":[9],"using":[10],"positive":[11],"cones.":[12],"show":[14,37],"that":[15,38],"such":[16],"orderings":[17],"coincide":[18],"with":[19],"total":[20],"order":[21],"relations":[22],"give":[24],"examples":[25],"of":[26,58,61],"(and":[28],"non":[29],"ordered)":[30],"fields.":[33],"In":[34],"particular":[35],"we":[36],"polynomial":[39],"can":[41],"be":[42],"in":[44,64],"(at":[45],"least)":[46],"two":[47],"different":[48],"ways":[49],"[8,":[50],"5,":[51],"4,":[52],"9].":[53],"This":[54],"is":[55],"the":[56,59],"continuation":[57],"development":[60],"algebraic":[62],"hierarchy":[63],"Mizar":[65],"[2,":[66],"3].":[67]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}