{"id":"https://openalex.org/W2514770626","doi":"https://doi.org/10.1515/forma-2016-0007","title":"Conservation Rules of Direct Sum Decomposition of Groups","display_name":"Conservation Rules of Direct Sum Decomposition of Groups","publication_year":2016,"publication_date":"2016-03-01","ids":{"openalex":"https://openalex.org/W2514770626","doi":"https://doi.org/10.1515/forma-2016-0007","mag":"2514770626"},"language":"en","primary_location":{"id":"doi:10.1515/forma-2016-0007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0007","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/1/article-p81.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/24/1/article-p81.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005167371","display_name":"Kazuhisa Nakasho","orcid":"https://orcid.org/0000-0003-1110-4342"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhisa Nakasho","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015411968","display_name":"Hiroshi Yamazaki","orcid":"https://orcid.org/0000-0001-9434-2957"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Yamazaki","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048322538","display_name":"Hiroyuki Okazaki","orcid":"https://orcid.org/0009-0000-1022-361X"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroyuki Okazaki","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":["Shinshu University Nagano, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University Nagano, Japan","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137975476"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1512441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"1","first_page":"81","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","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/T11703","display_name":"Rings, Modules, and Algebras","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/T10849","display_name":"Finite Group Theory Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/decomposition","display_name":"Decomposition","score":0.7192703485488892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6458694934844971},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.519763171672821},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5075598955154419},{"id":"https://openalex.org/keywords/flattening","display_name":"Flattening","score":0.49073994159698486},{"id":"https://openalex.org/keywords/layering","display_name":"Layering","score":0.45417049527168274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32354581356048584},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24711912870407104},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.077507883310318},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07003876566886902},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05524551868438721}],"concepts":[{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.7192703485488892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6458694934844971},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.519763171672821},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5075598955154419},{"id":"https://openalex.org/C19444555","wikidata":"https://www.wikidata.org/wiki/Q212750","display_name":"Flattening","level":2,"score":0.49073994159698486},{"id":"https://openalex.org/C176055353","wikidata":"https://www.wikidata.org/wiki/Q1402114","display_name":"Layering","level":2,"score":0.45417049527168274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32354581356048584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24711912870407104},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.077507883310318},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07003876566886902},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05524551868438721},{"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/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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":3,"locations":[{"id":"doi:10.1515/forma-2016-0007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0007","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/1/article-p81.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:5b662092c00245a8b78f660bb3d7c61e","is_oa":false,"landing_page_url":"https://doaj.org/article/5b662092c00245a8b78f660bb3d7c61e","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 24, Iss 1, Pp 81-94 (2016)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/5492","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/5492","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1515/forma-2016-0007","is_oa":true,"landing_page_url":"https://doi.org/10.1515/forma-2016-0007","pdf_url":"https://content.sciendo.com/downloadpdf/journals/forma/24/1/article-p81.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":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2514770626.pdf","grobid_xml":"https://content.openalex.org/works/W2514770626.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W1127721947","https://openalex.org/W1541824250","https://openalex.org/W1543877612","https://openalex.org/W2098464720","https://openalex.org/W2118242375","https://openalex.org/W2143507504","https://openalex.org/W2150348213","https://openalex.org/W2163090560","https://openalex.org/W2295728669","https://openalex.org/W2777805251","https://openalex.org/W4230191592","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2364255229","https://openalex.org/W2053119319","https://openalex.org/W3189260464","https://openalex.org/W2049450268","https://openalex.org/W2366451163","https://openalex.org/W2334616087","https://openalex.org/W2076772710","https://openalex.org/W605625157","https://openalex.org/W3163663844","https://openalex.org/W1969854450"],"abstract_inverted_index":{"Summary":[0],"In":[1,16,32],"this":[2],"article,":[3],"conservation":[4],"rules":[5],"of":[6,11,44,53,58,63],"the":[7,17,33,39,42,51,54,76],"direct":[8,45,59,64],"sum":[9,46],"decomposition":[10,47],"groups":[12],"are":[13],"mainly":[14],"discussed.":[15],"first":[18],"section,":[19],"we":[20,37],"prepare":[21],"miscellaneous":[22],"definitions":[23],"and":[24,61,73],"theorems":[25],"for":[26],"further":[27],"formalization":[28],"in":[29,75],"Mizar":[30],"[5].":[31],"next":[34],"three":[35],"sections,":[36],"formalized":[38],"fact":[40],"that":[41],"property":[43],"is":[48],"preserved":[49],"against":[50],"substitutions":[52],"subscript":[55],"set,":[56],"flattening":[57],"sum,":[60,65],"layering":[62],"respectively.":[66],"We":[67],"referred":[68],"to":[69],"[14],":[70],"[13]":[71],"[6]":[72],"[11]":[74],"formalization.":[77]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2016-09-16T00:00:00"}
