{"id":"https://openalex.org/W7225745027","doi":"https://doi.org/10.3390/math14224128","title":"Many-Sorted Algebraic Semantics for Dimensional Quantity Calculus","display_name":"Many-Sorted Algebraic Semantics for Dimensional Quantity Calculus","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225745027","doi":"https://doi.org/10.3390/math14224128"},"language":"en","primary_location":{"id":"doi:10.3390/math14224128","doi":"https://doi.org/10.3390/math14224128","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224128","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14224128","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009197300","display_name":"K. Yaji","orcid":"https://orcid.org/0000-0001-9900-3049","observed_orcids":["https://orcid.org/0000-0001-9900-3049"]},"institutions":[{"id":"https://openalex.org/I1298590031","display_name":"Shizuoka University","ror":"https://ror.org/01w6wtk13","country_code":"JP","type":"education","lineage":["https://openalex.org/I1298590031"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kohei Yaji","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Shizuoka University, 3-5-1 Johoku, Chuo-ku, Hamamatsu 432-8561, Japan"],"raw_orcid":"https://orcid.org/0000-0001-9900-3049","affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Shizuoka University, 3-5-1 Johoku, Chuo-ku, Hamamatsu 432-8561, Japan","institution_ids":["https://openalex.org/I1298590031"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009197300"],"corresponding_institution_ids":["https://openalex.org/I1298590031"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"22","first_page":"4128","last_page":"4128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.39329999685287476,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.39329999685287476,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.16300000250339508,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.14810000360012054,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8669000267982483},{"id":"https://openalex.org/C27859207","wikidata":"https://www.wikidata.org/wiki/Q5500180","display_name":"Free algebra","level":5,"score":0.6650999784469604},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6255000233650208},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.6205000281333923},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.6071000099182129},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5333999991416931},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47780001163482666},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.46939998865127563},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45339998602867126},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.43459999561309814},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.43160000443458557},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4140999913215637},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.4027999937534332},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.39649999141693115},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.3880000114440918},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.3862999975681305},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38029998540878296},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.37950000166893005},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.36149999499320984},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.33970001339912415},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.3377000093460083},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.3287000060081482},{"id":"https://openalex.org/C16310669","wikidata":"https://www.wikidata.org/wiki/Q1347208","display_name":"Epimorphism","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C18364862","wikidata":"https://www.wikidata.org/wiki/Q579978","display_name":"Homological algebra","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.27219998836517334},{"id":"https://openalex.org/C33959348","wikidata":"https://www.wikidata.org/wiki/Q1630568","display_name":"Monad (category theory)","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C100036529","wikidata":"https://www.wikidata.org/wiki/Q1945067","display_name":"Monomorphism","level":3,"score":0.26600000262260437},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.2635999917984009},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/math14224128","doi":"https://doi.org/10.3390/math14224128","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224128","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/math14224128","doi":"https://doi.org/10.3390/math14224128","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14224128","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"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":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,57,80],"study":[1],"polynomial":[2,55],"expressions":[3,120],"with":[4,62,105,178],"physical":[5,154],"dimensions":[6],"and":[7,45,70,88,129,156,168,184],"the":[8,39,63,77,101,106,122,150,163,179],"effect":[9],"of":[10,65,85,97,121,152],"setting":[11],"an":[12,92],"invertible":[13,93],"reference":[14,95,157],"quantity":[15],"equal":[16,127],"to":[17],"one.":[18],"Dimensions":[19],"are":[20,126,136],"treated":[21],"as":[22],"sorts":[23],"indexed":[24],"by":[25,109],"a":[26,72,153],"finitely":[27,160],"generated":[28],"free":[29,40],"Abelian":[30],"group":[31],"D.":[32],"Using":[33],"standard":[34],"categorical":[35],"constructions,":[36],"we":[37],"describe":[38],"D-graded":[41,66],"commutative":[42,67],"real":[43,68,164,185],"algebra":[44],"its":[46,59],"induced":[47],"finitary":[48],"monad":[49],"TD.":[50],"Monad":[51],"multiplication":[52],"is":[53,111],"homogeneous":[54,94,116],"substitution.":[56],"identify":[58],"Eilenberg\u2013Moore":[60],"category":[61,64],"algebras":[69],"give":[71],"D-sorted":[73],"Lawvere":[74],"theory":[75],"for":[76,172,199],"same":[78,123,180],"structure.":[79],"then":[81],"distinguish":[82],"normalization,":[83],"coarsening":[84],"degree":[86,99,125,182],"labels,":[87],"specialization":[89,102,135],"u=1.":[90],"For":[91,159],"u":[96],"infinite-order":[98],"g,":[100],"map":[103],"A\u27f6A/(u\u22121),":[104],"quotient":[107],"graded":[108,174],"D/Zg,":[110],"injective":[112],"on":[113],"each":[114],"original":[115,124],"component.":[117],"Thus,":[118],"two":[119],"if":[128,131],"only":[130],"their":[132],"images":[133],"after":[134],"equal,":[137],"although":[138],"mixed-degree":[139],"information":[140],"may":[141],"be":[142],"lost.":[143],"An":[144],"equation-of-motion":[145],"example":[146],"illustrates":[147],"dimensional":[148],"typing,":[149],"imposition":[151],"relation,":[155],"specialization.":[158],"presented":[161],"models,":[162],"Nullstellensatz":[165],"yields":[166],"existence":[167],"joint":[169],"equation-detection":[170],"criteria":[171],"surjective":[173],"numerical":[175],"presentations.":[176,204],"Models":[177],"full":[181],"support":[183],"radical":[186],"relations":[187],"can":[188],"differ":[189],"in":[190,201],"both":[191],"properties.":[192],"A":[193],"corollary":[194],"gives":[195],"finite":[196],"algebraic":[197],"certificates":[198],"validity":[200],"all":[202],"such":[203]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}