{"id":"https://openalex.org/W7203720907","doi":"https://doi.org/10.48550/arxiv.2608.15974","title":"Symmetry of self-injective dimensions under the Auslander condition","display_name":"Symmetry of self-injective dimensions under the Auslander condition","publication_year":2026,"publication_date":"2026-08-16","ids":{"openalex":"https://openalex.org/W7203720907","doi":"https://doi.org/10.48550/arxiv.2608.15974"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.15974","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15974","pdf_url":"https://arxiv.org/pdf/2608.15974","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.15974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137216572","display_name":"Dawei Shen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shen, Dawei","raw_affiliation_strings":["School of Mathematics and Statistics , Henan University , Kaifeng , Henan 475004 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Henan University , Kaifeng , Henan 475004 , P. R. China","institution_ids":["https://openalex.org/I173899330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5137216572"],"corresponding_institution_ids":["https://openalex.org/I173899330"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9276999831199646,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9276999831199646,"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":0.04280000180006027,"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":0.01119999960064888,"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/commutative-noetherian-rings","display_name":"commutative Noetherian rings","score":0.8799999952316284},{"id":"https://openalex.org/keywords/local-finiteness","display_name":"local finiteness","score":0.7689999938011169}],"concepts":[{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.7452999949455261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7430999875068665},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6949999928474426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.664900004863739},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.6256999969482422},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5447999835014343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C96489954","wikidata":"https://www.wikidata.org/wiki/Q5570832","display_name":"Global dimension","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29820001125335693},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C2779291638","wikidata":"https://www.wikidata.org/wiki/Q1455736","display_name":"Local symmetry","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.15974","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15974","pdf_url":"https://arxiv.org/pdf/2608.15974","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.15974","doi":"https://doi.org/10.48550/arxiv.2608.15974","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.15974","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.15974","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.15974","pdf_url":"https://arxiv.org/pdf/2608.15974","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203720907.pdf","grobid_xml":"https://content.openalex.org/works/W7203720907.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7169827311"],"related_works":["https://openalex.org/W2057392732","https://openalex.org/W7171966419","https://openalex.org/W4389239069","https://openalex.org/W2011340459","https://openalex.org/W4416113455","https://openalex.org/W2053532873","https://openalex.org/W2142205373","https://openalex.org/W4417224503","https://openalex.org/W4322763458","https://openalex.org/W4324325337"],"abstract_inverted_index":{"Let":[0],"$A$":[1],"be":[2],"a":[3,7,13,36,48,57],"module-finite":[4],"algebra":[5],"over":[6],"commutative":[8],"Noetherian":[9],"ring.":[10],"We":[11],"give":[12],"local":[14,38],"criterion":[15,58],"for":[16,59],"the":[17,24,44,60],"$n$-Gorenstein":[18],"condition.":[19],"For":[20],"such":[21],"algebras":[22],"satisfying":[23],"Auslander":[25,45],"condition,":[26],"we":[27,41],"prove":[28],"that":[29],"finite":[30],"self-injective":[31],"dimension":[32],"is":[33],"symmetric.":[34],"Under":[35],"one-sided":[37],"finiteness":[39],"hypothesis,":[40],"further":[42],"characterize":[43],"condition":[46],"by":[47],"fiberwise":[49],"form":[50],"of":[51],"Iyama's":[52],"grade":[53],"bijection":[54],"and":[55],"obtain":[56],"Auslander--Gorenstein":[61],"property.":[62]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-19T00:00:00"}