{"id":"https://openalex.org/W4414776369","doi":"https://doi.org/10.3390/sym17101642","title":"On ps-Supplement Submodules","display_name":"On ps-Supplement Submodules","publication_year":2025,"publication_date":"2025-10-03","ids":{"openalex":"https://openalex.org/W4414776369","doi":"https://doi.org/10.3390/sym17101642"},"language":"en","primary_location":{"id":"doi:10.3390/sym17101642","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101642","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1642/pdf?version=1759477239","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/10/1642/pdf?version=1759477239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019452528","display_name":"\u0130rfan Soydan","orcid":"https://orcid.org/0000-0001-7032-6485"},"institutions":[{"id":"https://openalex.org/I70387731","display_name":"Amasya \u00dcniversitesi","ror":"https://ror.org/00sbx0y13","country_code":"TR","type":"education","lineage":["https://openalex.org/I70387731"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"\u0130rfan Soydan","raw_affiliation_strings":["Department of Mathematics, Institute of Science, Amasya University, 05100 Amasya, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-7032-6485","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Institute of Science, Amasya University, 05100 Amasya, Turkey","institution_ids":["https://openalex.org/I70387731"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082670019","display_name":"Erg\u00fcl T\u00fcrkmen","orcid":"https://orcid.org/0000-0002-7082-1176"},"institutions":[{"id":"https://openalex.org/I70387731","display_name":"Amasya \u00dcniversitesi","ror":"https://ror.org/00sbx0y13","country_code":"TR","type":"education","lineage":["https://openalex.org/I70387731"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erg\u00fcl T\u00fcrkmen","raw_affiliation_strings":["Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Amasya, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Art and Science, Amasya University, 05100 Amasya, Turkey","institution_ids":["https://openalex.org/I70387731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061256797","display_name":"Hashem Bordbar","orcid":"https://orcid.org/0000-0003-3871-217X"},"institutions":[{"id":"https://openalex.org/I192455894","display_name":"University of Nova Gorica","ror":"https://ror.org/00mw0tw28","country_code":"SI","type":"education","lineage":["https://openalex.org/I192455894"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Hashem Bordbar","raw_affiliation_strings":["Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia"],"raw_orcid":"https://orcid.org/0000-0003-3871-217X","affiliations":[{"raw_affiliation_string":"Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia","institution_ids":["https://openalex.org/I192455894"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061256797"],"corresponding_institution_ids":["https://openalex.org/I192455894"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.34049659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"10","first_page":"1642","last_page":"1642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","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"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9986000061035156,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9936000108718872,"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/intersection","display_name":"Intersection (aeronautics)","score":0.583899974822998},{"id":"https://openalex.org/keywords/flat-module","display_name":"Flat module","score":0.513700008392334},{"id":"https://openalex.org/keywords/projective-module","display_name":"Projective module","score":0.5044999718666077},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.39719998836517334},{"id":"https://openalex.org/keywords/socle","display_name":"Socle","score":0.3783999979496002},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.373199999332428},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.3634999990463257},{"id":"https://openalex.org/keywords/injective-module","display_name":"Injective module","score":0.32600000500679016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7307999730110168},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.583899974822998},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5396000146865845},{"id":"https://openalex.org/C148896618","wikidata":"https://www.wikidata.org/wiki/Q1426191","display_name":"Flat module","level":4,"score":0.513700008392334},{"id":"https://openalex.org/C32268108","wikidata":"https://www.wikidata.org/wiki/Q942423","display_name":"Projective module","level":3,"score":0.5044999718666077},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C2776306272","wikidata":"https://www.wikidata.org/wiki/Q7553048","display_name":"Socle","level":4,"score":0.3783999979496002},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.373199999332428},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33239999413490295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C99463465","wikidata":"https://www.wikidata.org/wiki/Q2716519","display_name":"Injective module","level":3,"score":0.32600000500679016},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C130430149","wikidata":"https://www.wikidata.org/wiki/Q1292333","display_name":"Free module","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3086000084877014},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C31937215","wikidata":"https://www.wikidata.org/wiki/Q956233","display_name":"Simple module","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.2793999910354614}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17101642","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101642","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1642/pdf?version=1759477239","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:repozitorij.ung.si:IzpisGradiva.php?id=10651","is_oa":true,"landing_page_url":"https://repozitorij.ung.si/Dokument.php?id=34022&dn=","pdf_url":"https://repozitorij.ung.si/Dokument.php?id=34019&dn=","source":{"id":"https://openalex.org/S7407055115","display_name":"RUNG","issn_l":null,"issn":null,"is_oa":false,"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":"NA, Symmetry, vol. 17, no. 10,   1642, pp. 1-17, 2025.","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.3390/sym17101642","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17101642","pdf_url":"https://www.mdpi.com/2073-8994/17/10/1642/pdf?version=1759477239","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2968762207","display_name":null,"funder_award_id":"123F236","funder_id":"https://openalex.org/F4320322626","funder_display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu"},{"id":"https://openalex.org/G7530123626","display_name":null,"funder_award_id":"P2-0103","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"},{"id":"https://openalex.org/F4320322626","display_name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu","ror":"https://ror.org/04w9kkr77"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414776369.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W361181535","https://openalex.org/W1416433259","https://openalex.org/W1988066974","https://openalex.org/W2015541465","https://openalex.org/W2026025775","https://openalex.org/W2031038286","https://openalex.org/W2048434723","https://openalex.org/W2071696138","https://openalex.org/W2089546709","https://openalex.org/W2089627326","https://openalex.org/W2105958746","https://openalex.org/W2328559412","https://openalex.org/W2989758705","https://openalex.org/W2996023662","https://openalex.org/W2997279066","https://openalex.org/W4211164848","https://openalex.org/W4235731883","https://openalex.org/W4292255001"],"related_works":[],"abstract_inverted_index":{"In":[0,71],"this":[1,79],"work,":[2],"we":[3,73,91],"introduce":[4],"ps-supplement":[5,25,64],"submodules":[6],"as":[7,23],"a":[8,13,17,24,63,68,94,98],"kind":[9],"of":[10,16,52,56,78,84],"supplements.":[11],"Specifically,":[12],"submodule":[14,30],"V":[15],"module":[18],"M":[19],"is":[20,39,62,97,111],"referred":[21],"to":[22],"if":[26,104,107],"there":[27],"exists":[28],"another":[29],"U\u2286M":[31],"such":[32],"that":[33,93],"M=U+V":[34],"and":[35,105],"the":[36,49,57,82,85,88],"intersection":[37],"U\u2229V":[38],"projective":[40],"semisimple.":[41],"We":[42],"demonstrate":[43],"that,":[44],"over":[45],"an":[46],"arbitrary":[47],"ring,":[48],"collection":[50],"PS":[51],"short":[53],"exact":[54],"sequences":[55],"form":[58],"0\u27f6M\u27f6\u03c8N\u27f6\u03d5K\u27f60,":[59],"where":[60],"Im(\u03c8)":[61],"in":[65],"N,":[66],"constitutes":[67],"proper":[69],"class.":[70],"addition,":[72],"explore":[74],"several":[75],"homological":[76],"aspects":[77],"class,":[80],"including":[81],"symmetry":[83],"relations":[86],"between":[87],"modules.":[89],"Finally,":[90],"provide":[92],"ring":[95],"R":[96],"left":[99,109],"SI-ring":[100],"with":[101],"essential":[102],"socle":[103],"only":[106],"every":[108],"R-module":[110],"ps-supplemented.":[112]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
