{"id":"https://openalex.org/W3082105571","doi":"https://doi.org/10.1142/s1793830920500603","title":"On perfect annihilator graphs of commutative rings","display_name":"On perfect annihilator graphs of commutative rings","publication_year":2020,"publication_date":"2020-08-27","ids":{"openalex":"https://openalex.org/W3082105571","doi":"https://doi.org/10.1142/s1793830920500603","mag":"3082105571"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830920500603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500603","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/A5025265493","display_name":"Sh. Ebrahimi","orcid":null},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sh. Ebrahimi","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011236167","display_name":"Abolfazl Tehranian","orcid":"https://orcid.org/0000-0002-5811-1139"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"A. Tehranian","raw_affiliation_strings":["Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103005788","display_name":"R. Nikandish","orcid":"https://orcid.org/0000-0002-5155-1983"},"institutions":[{"id":"https://openalex.org/I3131332631","display_name":"Jundi-Shapur University of Technology","ror":"https://ror.org/019f08v97","country_code":"IR","type":"education","lineage":["https://openalex.org/I3131332631"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"R. Nikandish","raw_affiliation_strings":["Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran","institution_ids":["https://openalex.org/I3131332631"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103005788"],"corresponding_institution_ids":["https://openalex.org/I3131332631"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23977579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"05","first_page":"2050060","last_page":"2050060"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9973999857902527,"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":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8494043946266174},{"id":"https://openalex.org/keywords/annihilator","display_name":"Annihilator","score":0.7340993881225586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.650027871131897},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.49883508682250977},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49737146496772766},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4364240765571594},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4081267714500427},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.3939213156700134},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24751147627830505},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.1610584855079651}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8494043946266174},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.7340993881225586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.650027871131897},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.49883508682250977},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49737146496772766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4364240765571594},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4081267714500427},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.3939213156700134},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24751147627830505},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.1610584855079651}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830920500603","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500603","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":9,"referenced_works":["https://openalex.org/W1891879092","https://openalex.org/W1975461789","https://openalex.org/W1987023204","https://openalex.org/W2002257546","https://openalex.org/W2320813351","https://openalex.org/W2590739821","https://openalex.org/W2595399821","https://openalex.org/W2730978185","https://openalex.org/W3141776272"],"related_works":["https://openalex.org/W2360081430","https://openalex.org/W4308298797","https://openalex.org/W3176434841","https://openalex.org/W4324270382","https://openalex.org/W3087081535","https://openalex.org/W3091977257","https://openalex.org/W4255963200","https://openalex.org/W2791802482","https://openalex.org/W2360590989","https://openalex.org/W3125030210"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,12,21,28,36,43,50,54,63,88,101],"see":[2,13,22,29,37,44,51,55,64,89,102],"text]":[3,14,30,38,52,56,90,103],"be":[4,15],"a":[5,77],"commutative":[6],"ring":[7],"with":[8,39,93],"identity,":[9],"and":[10,46,53,60],"let":[11],"the":[16,34,40,71],"set":[17,42],"of":[18,20,27,73,76,80],"zero-divisors":[19],"text].":[23,65],"The":[24],"annihilator":[25,74],"graph":[26,35],"is":[31,84,91,104],"defined":[32],"as":[33],"vertex":[41],"text],":[45],"two":[47],"distinct":[48],"vertices":[49],"are":[57],"adjacent":[58],"if":[59,62,87],"only":[61],"In":[66],"this":[67],"paper,":[68],"we":[69],"study":[70],"perfectness":[72],"graphs":[75],"vast":[78],"range":[79],"rings.":[81],"Indeed,":[82],"it":[83],"shown":[85],"that":[86],"reduced":[92],"finitely":[94],"many":[95],"minimal":[96],"primes":[97],"or":[98],"nonreduced,":[99],"then":[100],"perfect.":[105]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}