{"id":"https://openalex.org/W2800321353","doi":"https://doi.org/10.1145/3377006.3377012","title":"Intrinsic Factorization of Ideals in Dedekind Domains","display_name":"Intrinsic Factorization of Ideals in Dedekind Domains","publication_year":2019,"publication_date":"2019-10-19","ids":{"openalex":"https://openalex.org/W2800321353","doi":"https://doi.org/10.1145/3377006.3377012","mag":"2800321353"},"language":"en","primary_location":{"id":"doi:10.1145/3377006.3377012","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3377006.3377012","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1805.02289","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042303183","display_name":"Mawunyo Kofi Darkey-Mensah","orcid":"https://orcid.org/0000-0001-9938-2632"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I864159182","display_name":"University of Silesia in Katowice","ror":"https://ror.org/0104rcc94","country_code":"PL","type":"education","lineage":["https://openalex.org/I864159182"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Mawunyo Kofi Darkey-Mensah","raw_affiliation_strings":["Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","Univ. of Silesia, Katowice, Poland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","institution_ids":["https://openalex.org/I864159182","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Univ. of Silesia, Katowice, Poland#TAB#","institution_ids":["https://openalex.org/I864159182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044009169","display_name":"Przemys\u0142aw Koprowski","orcid":"https://orcid.org/0000-0003-0952-5738"},"institutions":[{"id":"https://openalex.org/I864159182","display_name":"University of Silesia in Katowice","ror":"https://ror.org/0104rcc94","country_code":"PL","type":"education","lineage":["https://openalex.org/I864159182"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Przemys\u0142aw Koprowski","raw_affiliation_strings":["Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","Univ. of Silesia, Katowice, Poland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Silesia, ul. Bankowa 14, 40-007 Katowice, Poland","institution_ids":["https://openalex.org/I864159182","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Univ. of Silesia, Katowice, Poland#TAB#","institution_ids":["https://openalex.org/I864159182"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042303183"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I864159182"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0438627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"170","issue":"3","first_page":"107","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9993000030517578,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9986000061035156,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8066869974136353},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.7946964502334595},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7477834224700928},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6715395450592041},{"id":"https://openalex.org/keywords/unique-factorization-domain","display_name":"Unique factorization domain","score":0.6623173952102661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6446641087532043},{"id":"https://openalex.org/keywords/factorization-of-polynomials","display_name":"Factorization of polynomials","score":0.5832430124282837},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.5635700821876526},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5161551237106323},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49007952213287354},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4505388140678406},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42807602882385254},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4197917580604553},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.4165738821029663},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3683602213859558},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2334774136543274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11877554655075073},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10292047262191772},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06606125831604004},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.05657857656478882}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8066869974136353},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.7946964502334595},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7477834224700928},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6715395450592041},{"id":"https://openalex.org/C185592164","wikidata":"https://www.wikidata.org/wiki/Q1052579","display_name":"Unique factorization domain","level":3,"score":0.6623173952102661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6446641087532043},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.5832430124282837},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.5635700821876526},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5161551237106323},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49007952213287354},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4505388140678406},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42807602882385254},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4197917580604553},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4165738821029663},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3683602213859558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2334774136543274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11877554655075073},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10292047262191772},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06606125831604004},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.05657857656478882},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/3377006.3377012","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3377006.3377012","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},{"id":"doi:10.3233/fi-2019-1865","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2019-1865","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1805.02289","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.02289","pdf_url":"https://arxiv.org/pdf/1805.02289","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2800321353","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1805.02289.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1805.02289","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1805.02289","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1805.02289","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1805.02289","pdf_url":"https://arxiv.org/pdf/1805.02289","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4000000059604645,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2800321353.pdf","grobid_xml":"https://content.openalex.org/works/W2800321353.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1556780236","https://openalex.org/W1976677460","https://openalex.org/W1989763544","https://openalex.org/W2071102429","https://openalex.org/W2489377303","https://openalex.org/W3021045375"],"related_works":["https://openalex.org/W2144640311","https://openalex.org/W2962801008","https://openalex.org/W2035583073","https://openalex.org/W2963046019","https://openalex.org/W3026292252","https://openalex.org/W2950937525","https://openalex.org/W2182880927","https://openalex.org/W1972746153","https://openalex.org/W2522193420","https://openalex.org/W2949161972","https://openalex.org/W1967974756","https://openalex.org/W1990753230","https://openalex.org/W3197325512","https://openalex.org/W2949436787","https://openalex.org/W2949717884","https://openalex.org/W3201600075","https://openalex.org/W3031110531","https://openalex.org/W2953171098","https://openalex.org/W3047471054","https://openalex.org/W2802229368"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,5],"generalization":[3],"of":[4,16,39,42],"polynomial":[6],"factorization":[7],"algorithm":[8],"that":[9,31],"works":[10],"with":[11],"ideals":[12],"in":[13,23,28,48],"maximal":[14],"orders":[15],"global":[17],"function":[18],"fields.":[19],"The":[20],"method":[21],"presented":[22],"this":[24],"paper":[25],"is":[26],"intrinsic":[27],"the":[29,37,40,45],"sense":[30],"it":[32],"does":[33],"not":[34],"depend":[35],"on":[36],"embedding":[38],"ring":[41],"polynomials":[43],"into":[44],"Dedekind":[46],"domain":[47],"question.":[49]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}