{"id":"https://openalex.org/W4415927703","doi":"https://doi.org/10.1145/3798129.3800752","title":"The Skolem Problem in Rings of Positive Characteristic","display_name":"The Skolem Problem in Rings of Positive Characteristic","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W4415927703","doi":"https://doi.org/10.1145/3798129.3800752"},"language":null,"primary_location":{"id":"doi:10.1145/3798129.3800752","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800752","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3798129.3800752","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014183475","display_name":"Ruiwen Dong","orcid":"https://orcid.org/0009-0007-4349-082X"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ruiwen Dong","raw_affiliation_strings":["University of Oxford, Oxford, United Kingdom"],"raw_orcid":"https://orcid.org/0009-0007-4349-082X","affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120268253","display_name":"Doron Shafrir","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Doron Shafrir","raw_affiliation_strings":["Ben-Gurion University of the Negev, Be\u2019er Sheva, Israel"],"raw_orcid":"https://orcid.org/0009-0008-6425-3898","affiliations":[{"raw_affiliation_string":"Ben-Gurion University of the Negev, Be\u2019er Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05283098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"323","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.6105999946594238,"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":0.6105999946594238,"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":0.20919999480247498,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.07859999686479568,"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/decidability","display_name":"Decidability","score":0.7497000098228455},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7279999852180481},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.7128999829292297},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.6620000004768372},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5516999959945679},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5228999853134155},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.476500004529953},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.45190000534057617},{"id":"https://openalex.org/keywords/noncommutative-ring","display_name":"Noncommutative ring","score":0.37220001220703125}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8087999820709229},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7497000098228455},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7279999852180481},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.7128999829292297},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.6620000004768372},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5228999853134155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5020999908447266},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4117000102996826},{"id":"https://openalex.org/C125225535","wikidata":"https://www.wikidata.org/wiki/Q7049224","display_name":"Noncommutative ring","level":3,"score":0.37220001220703125},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C2780390204","wikidata":"https://www.wikidata.org/wiki/Q1036595","display_name":"Blowing up","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C156923205","wikidata":"https://www.wikidata.org/wiki/Q2905043","display_name":"Principal ideal ring","level":4,"score":0.2705000042915344},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2612999975681305}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3798129.3800752","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800752","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2510.27603","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.27603","pdf_url":"https://arxiv.org/pdf/2510.27603","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.27603","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.27603","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1145/3798129.3800752","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3798129.3800752","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 58th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311981","display_name":"Magdalen College, University of Oxford","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1,19],"that":[2,20,109],"the":[3,77,110,137],"Skolem":[4],"Problem":[5],"is":[6,66,128],"decidable":[7],"in":[8,136],"finitely":[9],"generated":[10],"commutative":[11,33],"rings":[12],"of":[13,30,40,80,100,113,121,133,139],"positive":[14],"characteristic.":[15],"More":[16],"precisely,":[17],"we":[18],"there":[21],"exists":[22],"an":[23],"algorithm":[24],"which,":[25],"given":[26],"a":[27,31,46,61,114,119,130],"finite":[28,131],"presentation":[29],"(unitary)":[32],"ring":[34,120],"R":[35],"=":[36,124],"\u2124/T[X1,":[37],"\u2026,":[38],"Xn]/I":[39],"characteristic":[41,122],"T":[42,123],">":[43],"0,":[44],"and":[45,73,86,91],"linear":[47,96,115],"recurrence":[48,116],"sequence":[49,117],"(\u03b3n)n":[50,57],"\u2208":[51,53,58],"\u2115":[52,59],"R\u2115,":[54],"determines":[55],"whether":[56],"contains":[60],"zero":[62,111],"term.":[63],"Our":[64,105],"proof":[65],"based":[67],"on":[68,76,94],"two":[69,101],"recent":[70],"results:":[71],"Dong":[72],"Shafrir":[74],"(2026)":[75],"solution":[78],"set":[79,112],"S-unit":[81],"equations":[82,97],"over":[83,98,118],"pe-torsion":[84],"modules,":[85],"Karimov,":[87],"Luca,":[88],"Nieuwveld,":[89],"Ouaknine,":[90],"Worrell":[92],"(2025)":[93],"solving":[95],"powers":[99],"multiplicatively":[102],"independent":[103],"numbers.":[104],"result":[106],"implies,":[107],"moreover,":[108],"p1e1":[125],"\u22ef":[126],"pkek":[127],"effectively":[129],"union":[132],"pi-normal":[134],"sets":[135],"sense":[138],"Derksen":[140],"(2007).":[141]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-05T00:00:00"}