{"id":"https://openalex.org/W2011577612","doi":"https://doi.org/10.1145/1277548.1277555","title":"Nonassociative structures on polynomial algebras arising from bio-operations on formal languages","display_name":"Nonassociative structures on polynomial algebras arising from bio-operations on formal languages","publication_year":2007,"publication_date":"2007-07-29","ids":{"openalex":"https://openalex.org/W2011577612","doi":"https://doi.org/10.1145/1277548.1277555","mag":"2011577612"},"language":"en","primary_location":{"id":"doi:10.1145/1277548.1277555","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277555","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5081627694","display_name":"Murray R. Bremner","orcid":"https://orcid.org/0000-0003-2672-3189"},"institutions":[{"id":"https://openalex.org/I32625721","display_name":"University of Saskatchewan","ror":"https://ror.org/010x8gc63","country_code":"CA","type":"education","lineage":["https://openalex.org/I32625721"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Murray R. Bremner","raw_affiliation_strings":["University of Saskatchewan, Saskatoon, SK, Canada"],"affiliations":[{"raw_affiliation_string":"University of Saskatchewan, Saskatoon, SK, Canada","institution_ids":["https://openalex.org/I32625721"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061537598","display_name":"Michael J. Hancock","orcid":null},"institutions":[{"id":"https://openalex.org/I32625721","display_name":"University of Saskatchewan","ror":"https://ror.org/010x8gc63","country_code":"CA","type":"education","lineage":["https://openalex.org/I32625721"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael J. Hancock","raw_affiliation_strings":["University of Saskatchewan, Saskatoon, SK, Canada"],"affiliations":[{"raw_affiliation_string":"University of Saskatchewan, Saskatoon, SK, Canada","institution_ids":["https://openalex.org/I32625721"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011988458","display_name":"Yunfeng Piao","orcid":null},"institutions":[{"id":"https://openalex.org/I32625721","display_name":"University of Saskatchewan","ror":"https://ror.org/010x8gc63","country_code":"CA","type":"education","lineage":["https://openalex.org/I32625721"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yunfeng Piao","raw_affiliation_strings":["University of Saskatchewan, Saskatoon, SK, Canada"],"affiliations":[{"raw_affiliation_string":"University of Saskatchewan, Saskatoon, SK, Canada","institution_ids":["https://openalex.org/I32625721"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081627694"],"corresponding_institution_ids":["https://openalex.org/I32625721"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.11588731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"41","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9943000078201294,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9943000078201294,"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/T11567","display_name":"semigroups and automata theory","score":0.9865999817848206,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9861000180244446,"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/multiset","display_name":"Multiset","score":0.7310699820518494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6474084258079529},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6465081572532654},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.6315314769744873},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6221878528594971},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.5852277874946594},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5691226720809937},{"id":"https://openalex.org/keywords/free-algebra","display_name":"Free algebra","score":0.5364817380905151},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5184537768363953},{"id":"https://openalex.org/keywords/free-monoid","display_name":"Free monoid","score":0.4857221245765686},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47140029072761536},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47009512782096863},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4084242284297943},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3599013686180115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33678293228149414},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.2687207758426666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23260214924812317},{"id":"https://openalex.org/keywords/cellular-algebra","display_name":"Cellular algebra","score":0.11446774005889893}],"concepts":[{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.7310699820518494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6474084258079529},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6465081572532654},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.6315314769744873},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6221878528594971},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5852277874946594},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5691226720809937},{"id":"https://openalex.org/C27859207","wikidata":"https://www.wikidata.org/wiki/Q5500180","display_name":"Free algebra","level":5,"score":0.5364817380905151},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5184537768363953},{"id":"https://openalex.org/C149685015","wikidata":"https://www.wikidata.org/wiki/Q5500266","display_name":"Free monoid","level":3,"score":0.4857221245765686},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47140029072761536},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47009512782096863},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4084242284297943},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3599013686180115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33678293228149414},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.2687207758426666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23260214924812317},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.11446774005889893},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277548.1277555","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277555","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1538534850","https://openalex.org/W1561605958","https://openalex.org/W1968643046","https://openalex.org/W2011519760","https://openalex.org/W2051148512","https://openalex.org/W2128687423","https://openalex.org/W2137261954"],"related_works":["https://openalex.org/W51936586","https://openalex.org/W2071633178","https://openalex.org/W2375401910","https://openalex.org/W3161268522","https://openalex.org/W2383679568","https://openalex.org/W2018277027","https://openalex.org/W2078404520","https://openalex.org/W2942660486","https://openalex.org/W4388685077","https://openalex.org/W4301971423"],"abstract_inverted_index":{"We":[0,73],"consider":[1],"sequential":[2],"insertion":[3,8],"and":[4,6,9],"deletion,":[5,10],"contextual":[7],"on":[11,56,71],"the":[12,23,40,50,75],"free":[13],"monoid":[14],"\u03a3":[15,17],"where":[16],"=":[18],"{x};":[19],"in":[20],"each":[21,54],"case":[22],"result":[24],"can":[25],"be":[26],"regarded":[27],"as":[28],"either":[29],"a":[30,33,62],"set":[31],"or":[32,69],"multiset.":[34],"Over":[35],"any":[36],"coefficient":[37],"field":[38],"F":[39],"vector":[41],"space":[42],"with":[43],"basis":[44],"\u03a3*":[45,57],"is":[46],"linearly":[47],"isomorphic":[48],"to":[49,60],"polynomial":[51,76],"algebra":[52,64],"F[x];":[53],"operation":[55],"extends":[58],"bilinearly":[59],"give":[61],"new":[63],"structure":[65],"(not":[66],"necessarily":[67],"commutative":[68],"associative)":[70],"F[x].":[72],"determine":[74],"identities":[77],"of":[78],"degree":[79],"\u2264":[80],"5":[81],"satisfied":[82],"by":[83],"these":[84],"structures.":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
