{"id":"https://openalex.org/W2086855586","doi":"https://doi.org/10.1016/s0747-7171(88)80047-6","title":"Using Gr\u00f6bner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence","display_name":"Using Gr\u00f6bner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2086855586","doi":"https://doi.org/10.1016/s0747-7171(88)80047-6","mag":"2086855586"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(88)80047-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80047-6","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic 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/A5084330789","display_name":"David Shannon","orcid":null},"institutions":[{"id":"https://openalex.org/I78641905","display_name":"Transylvania University","ror":"https://ror.org/01h4hqc60","country_code":"US","type":"education","lineage":["https://openalex.org/I78641905"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David Shannon","raw_affiliation_strings":["Department of Mathematics, Transylvania University, Lexington, KY 40508, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Transylvania University, Lexington, KY 40508, U.S.A","institution_ids":["https://openalex.org/I78641905"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061486704","display_name":"Moss E. Sweedler","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Moss Sweedler","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY 14853, U.S.A","Department of Mathematics, Cornell University, Ithaca, NY 14853,U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY 14853, U.S.A","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY 14853,U.S.A","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084330789"],"corresponding_institution_ids":["https://openalex.org/I78641905"],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":null,"fwci":9.0118,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.98530087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"2-3","first_page":"267","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9991000294685364,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8658681511878967},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.7719327211380005},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.7705714702606201},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5106704831123352},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47462260723114014},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.4717192053794861},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4657861292362213},{"id":"https://openalex.org/keywords/algebra-homomorphism","display_name":"Algebra homomorphism","score":0.4628324806690216},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.458927184343338},{"id":"https://openalex.org/keywords/filtered-algebra","display_name":"Filtered algebra","score":0.45418843626976013},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.41027188301086426},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3845062851905823},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24441108107566833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8658681511878967},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.7719327211380005},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7705714702606201},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5106704831123352},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47462260723114014},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.4717192053794861},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4657861292362213},{"id":"https://openalex.org/C175316100","wikidata":"https://www.wikidata.org/wiki/Q3882299","display_name":"Algebra homomorphism","level":3,"score":0.4628324806690216},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.458927184343338},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.45418843626976013},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.41027188301086426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3845062851905823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24441108107566833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(88)80047-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(88)80047-6","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1481997196","https://openalex.org/W1484293352","https://openalex.org/W1559703615","https://openalex.org/W2018615018","https://openalex.org/W2031399497","https://openalex.org/W2077725083","https://openalex.org/W2494959931","https://openalex.org/W4233685614","https://openalex.org/W6628753219","https://openalex.org/W6629087156","https://openalex.org/W6655185796","https://openalex.org/W6820634450"],"related_works":["https://openalex.org/W1543518806","https://openalex.org/W4225873811","https://openalex.org/W4302775140","https://openalex.org/W2181028733","https://openalex.org/W2149726687","https://openalex.org/W2044209922","https://openalex.org/W2993669906","https://openalex.org/W2952642024","https://openalex.org/W4300269627","https://openalex.org/W2799088590"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}