{"id":"https://openalex.org/W4401005797","doi":"https://doi.org/10.1216/rmj.2024.54.843","title":"ON THE LINEAR-TYPE PROPERTY OF THE JACOBIAN IDEAL OF AFFINE PLANE CURVES","display_name":"ON THE LINEAR-TYPE PROPERTY OF THE JACOBIAN IDEAL OF AFFINE PLANE CURVES","publication_year":2024,"publication_date":"2024-06-01","ids":{"openalex":"https://openalex.org/W4401005797","doi":"https://doi.org/10.1216/rmj.2024.54.843"},"language":"en","primary_location":{"id":"doi:10.1216/rmj.2024.54.843","doi":"https://doi.org/10.1216/rmj.2024.54.843","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1216/rmj.2024.54.843","pdf_url":null,"source":{"id":"https://openalex.org/S118967163","display_name":"Rocky Mountain Journal of Mathematics","issn_l":"0035-7596","issn":["0035-7596","1945-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4320800688","host_organization_name":"Rocky Mountain Mathematics Consortium","host_organization_lineage":["https://openalex.org/P4320800688"],"host_organization_lineage_names":["Rocky Mountain Mathematics Consortium"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rocky Mountain Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5066627498","display_name":"Abbas Nasrollah Nejad","orcid":"https://orcid.org/0000-0003-0511-6099","observed_orcids":["https://orcid.org/0000-0003-0511-6099"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abbas Nasrollah Nejad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5105084053","display_name":"Parisa Solhi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parisa Solhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"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":"54","issue":"3","first_page":"843","last_page":"853"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9907000064849854,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9907000064849854,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.008999999612569809,"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/T11435","display_name":"Polynomial and algebraic computation","score":9.999999747378752e-05,"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/jacobian-ideal","display_name":"Jacobian ideal","score":0.9150000214576721},{"id":"https://openalex.org/keywords/rees-algebra","display_name":"Rees algebra","score":0.902999997138977},{"id":"https://openalex.org/keywords/symmetric-algebra","display_name":"symmetric algebra","score":0.9909999966621399},{"id":"https://openalex.org/keywords/singular-points","display_name":"singular points","score":0.7080000042915344},{"id":"https://openalex.org/keywords/multiplicity-of-singularities","display_name":"multiplicity of singularities","score":0.7039999961853027},{"id":"https://openalex.org/keywords/noetherian-rings","display_name":"Noetherian rings","score":0.7620000243186951}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9254674911499023},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8434628248214722},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7369310259819031},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6773605942726135},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5633258819580078},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5517093539237976},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4463658034801483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43767985701560974},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42619821429252625},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4221426248550415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30027008056640625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1620127558708191},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0915963351726532},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1216/rmj.2024.54.843","doi":"https://doi.org/10.1216/rmj.2024.54.843","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1216/rmj.2024.54.843","pdf_url":null,"source":{"id":"https://openalex.org/S118967163","display_name":"Rocky Mountain Journal of Mathematics","issn_l":"0035-7596","issn":["0035-7596","1945-3795"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4320800688","host_organization_name":"Rocky Mountain Mathematics Consortium","host_organization_lineage":["https://openalex.org/P4320800688"],"host_organization_lineage_names":["Rocky Mountain Mathematics Consortium"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Rocky Mountain Journal of Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1654385827","https://openalex.org/W2039517653","https://openalex.org/W2081947803","https://openalex.org/W2366768275","https://openalex.org/W2791021700","https://openalex.org/W2910254770","https://openalex.org/W2963059802","https://openalex.org/W2963668257","https://openalex.org/W3104440602","https://openalex.org/W4214883536"],"related_works":["https://openalex.org/W2910254770","https://openalex.org/W1555022215","https://openalex.org/W4282932683","https://openalex.org/W7005792740","https://openalex.org/W2575453618","https://openalex.org/W2791021700","https://openalex.org/W1582993706","https://openalex.org/W593680289","https://openalex.org/W1998481874","https://openalex.org/W2892150199"],"abstract_inverted_index":{"An":[0],"ideal":[1,32,60],"I":[2,18],"in":[3],"a":[4],"Noetherian":[5],"ring":[6],"R":[7],"is":[8,19,44,61],"called":[9],"of":[10,17,25,33,41,45,55,62],"linear":[11,46,63],"type":[12],"if":[13],"the":[14,22,30],"Rees":[15],"algebra":[16,24],"isomorphic":[20],"to":[21],"symmetric":[23],"I.":[26],"We":[27,48],"prove":[28],"that":[29],"Jacobian":[31,59],"any":[34],"reduced":[35],"plane":[36,50],"curve":[37],"with":[38,52],"singular":[39,53],"points":[40,54],"multiplicity":[42,56],"2":[43],"type.":[47,64],"characterize":[49],"curves":[51],"3":[57],"whose":[58]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2024-07-26T00:00:00"}
