{"id":"https://openalex.org/W4408190193","doi":"https://doi.org/10.3390/sym17030398","title":"Nearly Complete Generalized Clifford Monoids and Applications","display_name":"Nearly Complete Generalized Clifford Monoids and Applications","publication_year":2025,"publication_date":"2025-03-06","ids":{"openalex":"https://openalex.org/W4408190193","doi":"https://doi.org/10.3390/sym17030398"},"language":"en","primary_location":{"id":"doi:10.3390/sym17030398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030398","pdf_url":"https://www.mdpi.com/2073-8994/17/3/398/pdf?version=1741259645","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/3/398/pdf?version=1741259645","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043680743","display_name":"Dilawar Juneed Mir","orcid":null},"institutions":[{"id":"https://openalex.org/I101407740","display_name":"Chandigarh University","ror":"https://ror.org/05t4pvx35","country_code":"IN","type":"education","lineage":["https://openalex.org/I101407740"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dilawar J. Mir","raw_affiliation_strings":["Department of Mathematics, CDOE, Chandigarh University, Mohali 140413, Punjab, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, CDOE, Chandigarh University, Mohali 140413, Punjab, India","institution_ids":["https://openalex.org/I101407740"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074414266","display_name":"Bana Al Subaiei","orcid":"https://orcid.org/0000-0001-6279-4959"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Bana Al Subaiei","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063514728","display_name":"Aftab Hussain Shah","orcid":"https://orcid.org/0000-0003-1143-0199"},"institutions":[{"id":"https://openalex.org/I76202665","display_name":"Central University of Kashmir","ror":"https://ror.org/03asvq815","country_code":"IN","type":"education","lineage":["https://openalex.org/I76202665"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Aftab H. Shah","raw_affiliation_strings":["Department of Mathematics, Central University of Kashmir, Ganderbal 191201, Jammu and Kashmir, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Central University of Kashmir, Ganderbal 191201, Jammu and Kashmir, India","institution_ids":["https://openalex.org/I76202665"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074414266"],"corresponding_institution_ids":["https://openalex.org/I4626487"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6516,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82195667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"3","first_page":"398","last_page":"398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9868000149726868,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.7391194701194763},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.7323511242866516},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.6701579093933105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6447563171386719},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.5330964922904968},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.47537389397621155},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46057581901550293},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.4557057321071625},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3853295147418976},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36596328020095825}],"concepts":[{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7391194701194763},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.7323511242866516},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6701579093933105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6447563171386719},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.5330964922904968},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.47537389397621155},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46057581901550293},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.4557057321071625},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3853295147418976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36596328020095825}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17030398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030398","pdf_url":"https://www.mdpi.com/2073-8994/17/3/398/pdf?version=1741259645","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"}],"best_oa_location":{"id":"doi:10.3390/sym17030398","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030398","pdf_url":"https://www.mdpi.com/2073-8994/17/3/398/pdf?version=1741259645","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408190193.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W781937223","https://openalex.org/W1990686507","https://openalex.org/W1997841430","https://openalex.org/W2095326676","https://openalex.org/W2141641421","https://openalex.org/W2157741016","https://openalex.org/W2326178355","https://openalex.org/W2331618806","https://openalex.org/W2885379725","https://openalex.org/W3157215754","https://openalex.org/W3216142546","https://openalex.org/W4247473027","https://openalex.org/W4309261695","https://openalex.org/W4389847917","https://openalex.org/W4394793584","https://openalex.org/W4399860504","https://openalex.org/W6829656510"],"related_works":["https://openalex.org/W3040709873","https://openalex.org/W4287814432","https://openalex.org/W4285749795","https://openalex.org/W3042339756","https://openalex.org/W3081419732","https://openalex.org/W2443808526","https://openalex.org/W2467965424","https://openalex.org/W2094117233","https://openalex.org/W4390714728","https://openalex.org/W1128915060"],"abstract_inverted_index":{"A":[0],"semigroup":[1,8,77],"S":[2],"is":[3],"termed":[4],"a":[5,13,26,58],"generalized":[6],"Clifford":[7],"(GC-semigroup)":[9],"if":[10],"it":[11],"forms":[12],"strong":[14],"semilattice":[15],"of":[16,42,61,67,76,80,120],"\u03c0-groups.":[17],"This":[18],"paper":[19],"explores":[20],"necessary":[21],"and":[22,65,94,111,118],"sufficient":[23],"conditions":[24],"for":[25,88,97],"GC-monoid":[27],"to":[28,72],"be":[29,48],"nearly":[30,121],"complete":[31,122],"within":[32],"certain":[33],"subclasses.":[34],"These":[35],"subclasses":[36],"are":[37],"distinguished":[38],"by":[39],"the":[40,62,73,115],"nature":[41],"their":[43],"linking":[44],"homomorphisms,":[45],"which":[46],"may":[47],"bijective,":[49],"surjective,":[50],"injective,":[51],"or":[52],"image":[53],"trivial.":[54],"The":[55,101],"findings":[56],"provide":[57],"deeper":[59],"understanding":[60],"structural":[63],"integrity":[64],"completeness":[66],"GC-monoids,":[68],"contributing":[69],"valuable":[70],"insights":[71],"theoretical":[74],"framework":[75],"theory.":[78],"Applications":[79],"this":[81],"study":[82],"span":[83],"various":[84],"fields,":[85],"including":[86],"cryptography":[87],"secure":[89],"algorithm":[90],"design,":[91],"coding":[92],"theory":[93],"quantum":[95,99],"computing":[96],"advanced":[98],"algorithms.":[100],"established":[102],"criteria":[103],"also":[104],"support":[105],"further":[106],"research":[107],"in":[108],"mathematical":[109],"biology":[110],"automorphic":[112],"theory,":[113],"demonstrating":[114],"broad":[116],"relevance":[117],"utility":[119],"GC-monoids.":[123]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-22T23:10:17.713674","created_date":"2025-10-10T00:00:00"}
