{"id":"https://openalex.org/W4224988872","doi":"https://doi.org/10.1142/s1793830922501051","title":"The extended graph of a module over a commutative ring","display_name":"The extended graph of a module over a commutative ring","publication_year":2022,"publication_date":"2022-04-28","ids":{"openalex":"https://openalex.org/W4224988872","doi":"https://doi.org/10.1142/s1793830922501051"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501051","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501051","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","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/A5021583199","display_name":"S. Babaei","orcid":"https://orcid.org/0000-0001-7039-2095"},"institutions":[{"id":"https://openalex.org/I69425150","display_name":"Imam Khomeini International University","ror":"https://ror.org/02jeykk09","country_code":"IR","type":"education","lineage":["https://openalex.org/I69425150"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"S. Babaei","raw_affiliation_strings":["Department of Mathematics, Imam Khomeini International University, Postal Code 34149-1-6818 Qazvin, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imam Khomeini International University, Postal Code 34149-1-6818 Qazvin, Iran","institution_ids":["https://openalex.org/I69425150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051158575","display_name":"Esra \u015eengelen Sevim","orcid":"https://orcid.org/0000-0003-1296-0845"},"institutions":[{"id":"https://openalex.org/I118036225","display_name":"Istanbul Bilgi University","ror":"https://ror.org/04pm4x478","country_code":"TR","type":"education","lineage":["https://openalex.org/I118036225"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"E. Sengelen Sevim","raw_affiliation_strings":["Eski Silahtara\u011fa Elektrik Santrali Kazim Karabekir, Istanbul Bilgi University, Cad. No. 2/1334060, Ey\u00fcp, Istanbul, Turkey"],"affiliations":[{"raw_affiliation_string":"Eski Silahtara\u011fa Elektrik Santrali Kazim Karabekir, Istanbul Bilgi University, Cad. No. 2/1334060, Ey\u00fcp, Istanbul, Turkey","institution_ids":["https://openalex.org/I118036225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021583199"],"corresponding_institution_ids":["https://openalex.org/I69425150"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11398644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":1.0,"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":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9912999868392944,"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":0.9839000105857849,"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/voltage-graph","display_name":"Voltage graph","score":0.6624817848205566},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.6541330218315125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5967820286750793},{"id":"https://openalex.org/keywords/annihilator","display_name":"Annihilator","score":0.5925074815750122},{"id":"https://openalex.org/keywords/null-graph","display_name":"Null graph","score":0.5283447504043579},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5172701478004456},{"id":"https://openalex.org/keywords/petersen-graph","display_name":"Petersen graph","score":0.4920584559440613},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.46810436248779297},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4617045521736145},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.43970999121665955},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42919057607650757},{"id":"https://openalex.org/keywords/zero-divisor","display_name":"Zero divisor","score":0.42354604601860046},{"id":"https://openalex.org/keywords/butterfly-graph","display_name":"Butterfly graph","score":0.4215046167373657},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.2334786057472229},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1671082079410553},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.15681365132331848}],"concepts":[{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.6624817848205566},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.6541330218315125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5967820286750793},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.5925074815750122},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.5283447504043579},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5172701478004456},{"id":"https://openalex.org/C28093856","wikidata":"https://www.wikidata.org/wiki/Q835614","display_name":"Petersen graph","level":5,"score":0.4920584559440613},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.46810436248779297},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4617045521736145},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.43970999121665955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42919057607650757},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.42354604601860046},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.4215046167373657},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.2334786057472229},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1671082079410553},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.15681365132331848}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501051","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501051","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"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":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1987023204","https://openalex.org/W2002257546","https://openalex.org/W2911086894","https://openalex.org/W2945179726","https://openalex.org/W2994514764","https://openalex.org/W4212819720"],"related_works":["https://openalex.org/W1964843613","https://openalex.org/W2782443879","https://openalex.org/W4285284031","https://openalex.org/W2034726607","https://openalex.org/W2954009223","https://openalex.org/W4280619628","https://openalex.org/W1999761254","https://openalex.org/W2371151138","https://openalex.org/W2048112267","https://openalex.org/W4385615536"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,45],"associate":[4],"a":[5,9,12],"simple":[6],"graph":[7,39,52,56],"to":[8],"module":[10],"over":[11],"commutative":[13],"ring":[14],"and":[15,53],"call":[16],"it":[17],"extended":[18,51],"graph,":[19],"that":[20],"adjacent":[21],"condition":[22],"depends":[23],"on":[24],"the":[25,32,37,50,54],"properties":[26],"of":[27,34,57],"annihilator":[28],"submodules.":[29],"We":[30],"determine":[31],"structure":[33],"modules,":[35],"when":[36],"associated":[38],"is":[40],"star":[41],"or":[42],"complete.":[43],"Moreover,":[44],"look":[46],"for":[47],"relationships":[48],"between":[49],"zero-divisor":[55],"modules.":[58]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}