{"id":"https://openalex.org/W2031551360","doi":"https://doi.org/10.1142/s0218196709005056","title":"OPENED MODULAR NUMERICAL SEMIGROUPS WITH A GIVEN MULTIPLICITY","display_name":"OPENED MODULAR NUMERICAL SEMIGROUPS WITH A GIVEN MULTIPLICITY","publication_year":2009,"publication_date":"2009-03-01","ids":{"openalex":"https://openalex.org/W2031551360","doi":"https://doi.org/10.1142/s0218196709005056","mag":"2031551360"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005056","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/A5090505051","display_name":"J. C. Rosales","orcid":"https://orcid.org/0000-0003-3353-4335"},"institutions":[{"id":"https://openalex.org/I173304897","display_name":"Universidad de Granada","ror":"https://ror.org/04njjy449","country_code":"ES","type":"education","lineage":["https://openalex.org/I173304897"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. C. ROSALES","raw_affiliation_strings":["Departamento de \u00c1lgebra, Universidad de Granada, E-18071 Granada, Spain","Departamento de Algebra, Universidad de Granada, E-18071 Granada, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de \u00c1lgebra, Universidad de Granada, E-18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]},{"raw_affiliation_string":"Departamento de Algebra, Universidad de Granada, E-18071 Granada, Spain","institution_ids":["https://openalex.org/I173304897"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040094936","display_name":"Paulo Vasco","orcid":"https://orcid.org/0000-0001-5460-4297"},"institutions":[{"id":"https://openalex.org/I155381812","display_name":"University of Tr\u00e1s-os-Montes and Alto Douro","ror":"https://ror.org/03qc8vh97","country_code":"PT","type":"education","lineage":["https://openalex.org/I155381812"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"P. VASCO","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Universidade de Tr\u00e1s-os-Montes e Alto, Douro, 5001-801 Vila Real, Portugal"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidade de Tr\u00e1s-os-Montes e Alto, Douro, 5001-801 Vila Real, Portugal","institution_ids":["https://openalex.org/I155381812"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090505051"],"corresponding_institution_ids":["https://openalex.org/I173304897"],"apc_list":null,"apc_paid":null,"fwci":1.5796,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80470016,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"02","first_page":"235","last_page":"246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9972000122070312,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9781000018119812,"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":0.9311364889144897},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.8910783529281616},{"id":"https://openalex.org/keywords/numerical-semigroup","display_name":"Numerical semigroup","score":0.8649081587791443},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5320661664009094},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4258945882320404},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.4197232127189636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3685206472873688},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3673097491264343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1223253607749939}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9311364889144897},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.8910783529281616},{"id":"https://openalex.org/C2779628518","wikidata":"https://www.wikidata.org/wiki/Q7069664","display_name":"Numerical semigroup","level":3,"score":0.8649081587791443},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5320661664009094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4258945882320404},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.4197232127189636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3685206472873688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3673097491264343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1223253607749939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005056","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005056","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W651067426","https://openalex.org/W1983044524","https://openalex.org/W2027021672","https://openalex.org/W2076720414","https://openalex.org/W2130680601","https://openalex.org/W2142231701","https://openalex.org/W2332901121"],"related_works":["https://openalex.org/W2522074991","https://openalex.org/W2007825160","https://openalex.org/W2153946164","https://openalex.org/W2953366618","https://openalex.org/W4289919814","https://openalex.org/W3193582865","https://openalex.org/W2768505255","https://openalex.org/W3041033841","https://openalex.org/W2940116067","https://openalex.org/W4285241108"],"abstract_inverted_index":{"Let":[0],"\u2115":[1],"be":[2,11],"the":[3,31,34,38,59,62,65],"set":[4],"of":[5,14,33,37,68,71],"nonnegative":[6],"integers":[7,48],"and":[8,45,64],"let":[9],"I":[10],"an":[12],"interval":[13],"positive":[15],"rational":[16],"numbers.":[17],"Then":[18],"[Formula:":[19,40],"see":[20,41,58],"text]":[21],"is":[22],"a":[23,44,53],"numerical":[24,35],"semigroup.":[25],"In":[26],"this":[27,69],"paper":[28],"we":[29],"study":[30],"multiplicity":[32,63],"semigroups":[36],"form":[39],"text],":[42],"where":[43],"b":[46],"are":[47],"such":[49],"that":[50],"2":[51],"\u2264":[52],"<":[54],"b.":[55],"We":[56],"also":[57],"connection":[60],"between":[61],"Frobenius":[66],"number":[67],"type":[70],"semigroups.":[72]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}