{"id":"https://openalex.org/W4390147688","doi":"https://doi.org/10.2478/forma-2023-0013","title":"Embedding Principle for Rings and Abelian Groups","display_name":"Embedding Principle for Rings and Abelian Groups","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4390147688","doi":"https://doi.org/10.2478/forma-2023-0013"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2023-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0013","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0013","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"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/forma-2023-0013","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070513311","display_name":"Yasushige Watase","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yasushige Watase","raw_affiliation_strings":["Suginami-ku Matsunoki 6 , Tokyo , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Suginami-ku Matsunoki 6 , Tokyo , Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070513311"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17956916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"1","first_page":"143","last_page":"150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11424","display_name":"Security and Verification in Computing","score":0.9732999801635742,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11424","display_name":"Security and Verification in Computing","score":0.9732999801635742,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.968500018119812,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/subring","display_name":"Subring","score":0.884395956993103},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7829974293708801},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.7190403938293457},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.717970073223114},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6857626438140869},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5469853281974792},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5231524705886841},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.48447322845458984},{"id":"https://openalex.org/keywords/ring-theory","display_name":"Ring theory","score":0.43699485063552856},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43290162086486816},{"id":"https://openalex.org/keywords/group-ring","display_name":"Group ring","score":0.4325960874557495},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40498030185699463},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.3254692852497101},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.28356844186782837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1062186062335968},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.06473588943481445}],"concepts":[{"id":"https://openalex.org/C21714298","wikidata":"https://www.wikidata.org/wiki/Q929536","display_name":"Subring","level":3,"score":0.884395956993103},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7829974293708801},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.7190403938293457},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.717970073223114},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6857626438140869},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5469853281974792},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5231524705886841},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.48447322845458984},{"id":"https://openalex.org/C196434610","wikidata":"https://www.wikidata.org/wiki/Q1208658","display_name":"Ring theory","level":4,"score":0.43699485063552856},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43290162086486816},{"id":"https://openalex.org/C76572486","wikidata":"https://www.wikidata.org/wiki/Q2602722","display_name":"Group ring","level":3,"score":0.4325960874557495},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40498030185699463},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3254692852497101},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.28356844186782837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1062186062335968},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.06473588943481445},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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":2,"locations":[{"id":"doi:10.2478/forma-2023-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0013","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0013","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:11320/15851","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/15851","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/15851/1/Embedding-Principle-for-Rings-and-Abelian-Groups.pdf","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2023-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2023-0013","pdf_url":"https://sciendo.com/pdf/10.2478/forma-2023-0013","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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390147688.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1968315351","https://openalex.org/W2295728669","https://openalex.org/W2526342011","https://openalex.org/W2770430340","https://openalex.org/W2953284898","https://openalex.org/W2963218298","https://openalex.org/W4233049353","https://openalex.org/W4313308179","https://openalex.org/W4321347232"],"related_works":["https://openalex.org/W2417312525","https://openalex.org/W4237093411","https://openalex.org/W2074829895","https://openalex.org/W2029767764","https://openalex.org/W154136091","https://openalex.org/W1971784388","https://openalex.org/W2076422811","https://openalex.org/W2255261250","https://openalex.org/W2035716819","https://openalex.org/W2329341187"],"abstract_inverted_index":{"Summary":[0],"The":[1],"article":[2],"concerns":[3],"about":[4],"formalizing":[5],"a":[6,21,27,33,45],"certain":[7],"lemma":[8],"on":[9],"embedding":[10],"of":[11],"algebraic":[12,51],"structures":[13,52],"in":[14,26],"the":[15],"Mizar":[16],"system,":[17],"claiming":[18],"that":[19],"if":[20],"ring":[22,28,34],"A":[23,43],"is":[24,37],"embedded":[25],"B":[29,40],"then":[30],"there":[31],"exists":[32],"C":[35],"which":[36],"isomorphic":[38],"to":[39,50],"and":[41,57],"includes":[42],"as":[44,54],"subring.":[46],"This":[47],"construction":[48],"applies":[49],"such":[53],"Abelian":[55],"groups":[56],"rings.":[58]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
