{"id":"https://openalex.org/W2076329201","doi":"https://doi.org/10.1142/s0218196713500185","title":"QUASI-ISOMETRY AND FINITE PRESENTATIONS OF LEFT CANCELLATIVE MONOIDS","display_name":"QUASI-ISOMETRY AND FINITE PRESENTATIONS OF LEFT CANCELLATIVE MONOIDS","publication_year":2013,"publication_date":"2013-04-25","ids":{"openalex":"https://openalex.org/W2076329201","doi":"https://doi.org/10.1142/s0218196713500185","mag":"2076329201"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196713500185","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713500185","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066454537","display_name":"Robert D. Gray","orcid":"https://orcid.org/0000-0002-7200-1745"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"ROBERT D. GRAY","raw_affiliation_strings":["Centro de \u00c1lgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649\u2013003 Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"Centro de \u00c1lgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649\u2013003 Lisboa, Portugal","institution_ids":["https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041232556","display_name":"Mark Kambites","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"MARK KAMBITES","raw_affiliation_strings":["School of Mathematics, University of Manchester, Manchester M13 9PL, England, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Manchester, Manchester M13 9PL, England, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066454537"],"corresponding_institution_ids":["https://openalex.org/I141596103"],"apc_list":null,"apc_paid":null,"fwci":2.2193,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.88111357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":"05","first_page":"1099","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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":0.9995999932289124,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9927999973297119,"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":0.8703931570053101},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.7173587083816528},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.6985158920288086},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.6638427972793579},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.6367363929748535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5586778521537781},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.5559579730033875},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.42152369022369385},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3529497981071472},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12455245852470398}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8703931570053101},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.7173587083816528},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.6985158920288086},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.6638427972793579},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.6367363929748535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5586778521537781},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.5559579730033875},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.42152369022369385},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3529497981071472},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12455245852470398},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196713500185","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196713500185","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:43155","is_oa":false,"landing_page_url":"https://ueaeprints.uea.ac.uk/id/eprint/43155/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4212162790","display_name":null,"funder_award_id":"EP/F014945/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W654957503","https://openalex.org/W1523977407","https://openalex.org/W1963727374","https://openalex.org/W2019672336","https://openalex.org/W2043045383","https://openalex.org/W2092082324","https://openalex.org/W2092410163","https://openalex.org/W2093120826","https://openalex.org/W2131917922","https://openalex.org/W2158446505","https://openalex.org/W4246980524","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1511851241","https://openalex.org/W2130856794","https://openalex.org/W1523052313","https://openalex.org/W1975351486","https://openalex.org/W365049119","https://openalex.org/W3106811412","https://openalex.org/W2079333248","https://openalex.org/W4310527795","https://openalex.org/W1978362621","https://openalex.org/W2058817145"],"abstract_inverted_index":{"We":[0,40],"show":[1,45],"that":[2,46,58],"being":[3,7],"finitely":[4,8,18],"presentable":[5,9],"and":[6,56],"with":[10],"solvable":[11,62],"word":[12,63],"problem":[13,64],"are":[14,65],"quasi-isometry":[15],"invariants":[16,68],"of":[17,33],"generated":[19],"left":[20,37],"cancellative":[21,38],"monoids.":[22,39,71],"Our":[23],"main":[24],"tool":[25],"is":[26],"an":[27],"elementary,":[28],"but":[29],"useful,":[30],"geometric":[31],"characterization":[32,48],"finite":[34],"presentability":[35],"for":[36,69],"also":[41],"give":[42],"examples":[43],"to":[44,52],"this":[47],"does":[49],"not":[50,66],"extend":[51],"monoids":[53],"in":[54],"general,":[55],"indeed":[57],"properties":[59],"such":[60],"as":[61],"isometry":[67],"general":[70]},"counts_by_year":[{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
