{"id":"https://openalex.org/W4391400180","doi":"https://doi.org/10.1142/s021819672450005x","title":"Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings","display_name":"Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings","publication_year":2024,"publication_date":"2024-01-31","ids":{"openalex":"https://openalex.org/W4391400180","doi":"https://doi.org/10.1142/s021819672450005x"},"language":"en","primary_location":{"id":"doi:10.1142/s021819672450005x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672450005x","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/A5009575000","display_name":"Rongmin Zhu","orcid":"https://orcid.org/0000-0002-1815-5954"},"institutions":[{"id":"https://openalex.org/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rongmin Zhu","raw_affiliation_strings":["School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-1815-5954","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101657618","display_name":"Haiyu Liu","orcid":"https://orcid.org/0000-0002-5612-397X"},"institutions":[{"id":"https://openalex.org/I4210144214","display_name":"Jiangsu University of Technology","ror":"https://ror.org/04jabhf80","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210144214"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiyu Liu","raw_affiliation_strings":["School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, P. R. China"],"raw_orcid":"https://orcid.org/0000-0002-5612-397X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, P. R. China","institution_ids":["https://openalex.org/I4210144214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009575000"],"corresponding_institution_ids":["https://openalex.org/I119045251"],"apc_list":null,"apc_paid":null,"fwci":1.9124,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.80563745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"34","issue":"02","first_page":"175","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998999834060669,"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":0.9998999834060669,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.9334031939506531},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6517928242683411},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.5787950754165649},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5461907386779785},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5119948983192444},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40841618180274963},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.406765341758728},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32201188802719116},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.06905865669250488}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9334031939506531},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6517928242683411},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.5787950754165649},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5461907386779785},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5119948983192444},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40841618180274963},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.406765341758728},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32201188802719116},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.06905865669250488},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819672450005x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672450005x","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":[{"id":"https://openalex.org/G6081217784","display_name":null,"funder_award_id":"2023J05048","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G8574546914","display_name":null,"funder_award_id":"12201223","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1988612565","https://openalex.org/W1989436714","https://openalex.org/W1993186705","https://openalex.org/W1994755797","https://openalex.org/W2005339632","https://openalex.org/W2033787979","https://openalex.org/W2054193886","https://openalex.org/W2067776176","https://openalex.org/W2075424595","https://openalex.org/W2095625701","https://openalex.org/W2103673798","https://openalex.org/W2114145385","https://openalex.org/W2155303182","https://openalex.org/W2240732280","https://openalex.org/W2278560913","https://openalex.org/W2501818278","https://openalex.org/W2799045271","https://openalex.org/W2962942383","https://openalex.org/W2964167100","https://openalex.org/W2964261192","https://openalex.org/W2969101043","https://openalex.org/W2990302147","https://openalex.org/W3036012179","https://openalex.org/W3042118363","https://openalex.org/W3086387981","https://openalex.org/W3123445303","https://openalex.org/W3127228769","https://openalex.org/W3159875415","https://openalex.org/W4243046450","https://openalex.org/W4243423581","https://openalex.org/W4300662053","https://openalex.org/W4311069419"],"related_works":["https://openalex.org/W4387323617","https://openalex.org/W2131364695","https://openalex.org/W4245693476","https://openalex.org/W3112482275","https://openalex.org/W1987509617","https://openalex.org/W1489491826","https://openalex.org/W2023329664","https://openalex.org/W1967452912","https://openalex.org/W1964808438","https://openalex.org/W4308012852"],"abstract_inverted_index":{"Let":[0],"A":[1,30],"and":[2,6,31,99],"B":[3],"be":[4],"rings":[5],"[Formula:":[7,21,53,91],"see":[8,22,54,92],"text]":[9,23],"with":[10,47,88],"M":[11],"an":[12,78],"A-B-bimodule.":[13],"We":[14],"first":[15],"construct":[16,96],"a":[17,38,61,85],"semi-complete":[18],"duality":[19,27,51],"pair":[20,52],"over":[24,29],"T":[25],"using":[26],"pairs":[28],"B,":[32],"respectively.":[33],"Then":[34],"we":[35,58,76,95],"characterize":[36],"when":[37,60],"left":[39,62,86],"T-module":[40,63,87],"is":[41,64],"Gorenstein":[42,67,72,81,105],"projective,":[43],"injective":[44,70],"or":[45,71],"flat":[46,82],"respect":[48,89],"to":[49,90,102],"the":[50],"text].":[55,93],"As":[56],"applications,":[57],"investigate":[59],"projectively":[65],"coresolved":[66],"flat,":[68],"Ding":[69],"flat.":[73],"In":[74],"addition,":[75],"give":[77],"estimate":[79],"of":[80,84],"dimension":[83],"Finally,":[94],"model":[97],"structures":[98],"recollements":[100],"relative":[101],"these":[103],"generalized":[104],"modules.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
