{"id":"https://openalex.org/W2940364010","doi":"https://doi.org/10.3390/sym11040553","title":"Involution Abel\u2013Grassmann\u2019s Groups and Filter Theory of Abel\u2013Grassmann\u2019s Groups","display_name":"Involution Abel\u2013Grassmann\u2019s Groups and Filter Theory of Abel\u2013Grassmann\u2019s Groups","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2940364010","doi":"https://doi.org/10.3390/sym11040553","mag":"2940364010"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040553","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040553","pdf_url":"https://www.mdpi.com/2073-8994/11/4/553/pdf?version=1555498214","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/4/553/pdf?version=1555498214","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100330121","display_name":"Xiaohong Zhang","orcid":"https://orcid.org/0000-0003-2320-0884"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaohong Zhang","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047648829","display_name":"Xiaoying Wu","orcid":"https://orcid.org/0000-0003-0144-8440"},"institutions":[{"id":"https://openalex.org/I51622183","display_name":"Shaanxi University of Science and Technology","ror":"https://ror.org/034t3zs45","country_code":"CN","type":"education","lineage":["https://openalex.org/I51622183"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoying Wu","raw_affiliation_strings":["Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shaanxi University of Science & Technology, Xi\u2019an 710021, China","institution_ids":["https://openalex.org/I51622183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100330121"],"corresponding_institution_ids":["https://openalex.org/I51622183"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4116,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66763404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"4","first_page":"553","last_page":"553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9973999857902527,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9782000184059143,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9559999704360962,"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":0.8573359847068787},{"id":"https://openalex.org/keywords/involution","display_name":"Involution (esoterism)","score":0.794910192489624},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6191130876541138},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5715599060058594},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.553298830986023},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5395886301994324},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3414774239063263}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8573359847068787},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.794910192489624},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6191130876541138},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5715599060058594},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.553298830986023},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5395886301994324},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3414774239063263},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11040553","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040553","pdf_url":"https://www.mdpi.com/2073-8994/11/4/553/pdf?version=1555498214","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c5c19e039f464676bb3786f9dd36bf5e","is_oa":true,"landing_page_url":"https://doaj.org/article/c5c19e039f464676bb3786f9dd36bf5e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 553 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11040553","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040553","pdf_url":"https://www.mdpi.com/2073-8994/11/4/553/pdf?version=1555498214","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2940364010.pdf","grobid_xml":"https://content.openalex.org/works/W2940364010.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W186521386","https://openalex.org/W1487875360","https://openalex.org/W1912094607","https://openalex.org/W2034588518","https://openalex.org/W2049401522","https://openalex.org/W2116694668","https://openalex.org/W2499469294","https://openalex.org/W2517034171","https://openalex.org/W2612805960","https://openalex.org/W2806618176","https://openalex.org/W2890183553","https://openalex.org/W2896017664","https://openalex.org/W2899482720","https://openalex.org/W2919603292","https://openalex.org/W2922493167","https://openalex.org/W2947670988","https://openalex.org/W3092455146","https://openalex.org/W3106133900","https://openalex.org/W4251673450","https://openalex.org/W6640019380"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4308159138","https://openalex.org/W4327811209","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W2914794208","https://openalex.org/W3037616202","https://openalex.org/W2963079901","https://openalex.org/W2061863373","https://openalex.org/W2767147306"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"some":[3,15],"basic":[4],"properties":[5],"and":[6,22,26,38,52,56,84,89],"structure":[7,58,88],"characterizations":[8],"of":[9,17,35,60,69,71],"AG-groups":[10,19,28,53,63],"are":[11,20,29,42,54,64,92],"further":[12],"studied.":[13],"First,":[14],"examples":[16],"infinite":[18],"given,":[21],"weak":[23],"commutative,":[24],"alternative":[25],"quasi-cancellative":[27],"discussed.":[30],"Second,":[31],"two":[32],"new":[33],"concepts":[34],"involution":[36,40,48,62],"AG-group":[37,41,73],"generalized":[39],"proposed,":[43],"the":[44,57,67,76,85],"relationships":[45],"among":[46],"(generalized)":[47,61],"AG-groups,":[49],"commutative":[50],"groups":[51],"investigated,":[55],"theorems":[59,91],"proved.":[65],"Third,":[66],"notion":[68],"filter":[70],"an":[72],"is":[74,79],"introduced,":[75],"congruence":[77],"relation":[78],"constructed":[80],"from":[81],"arbitrary":[82],"filter,":[83],"corresponding":[86],"quotient":[87],"homomorphism":[90],"established.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}