{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:38:38Z","timestamp":1740155918382,"version":"3.37.3"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with identity, and let [Formula: see text] be the set of zero-divisors of [Formula: see text]. The annihilator graph of [Formula: see text] is defined as the graph [Formula: see text] with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we study the perfectness of annihilator graphs of a vast range of rings. Indeed, it is shown that if [Formula: see text] is reduced with finitely many minimal primes or nonreduced, then [Formula: see text] is perfect. <\/jats:p>","DOI":"10.1142\/s1793830920500603","type":"journal-article","created":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T09:13:32Z","timestamp":1598519612000},"page":"2050060","source":"Crossref","is-referenced-by-count":0,"title":["On perfect annihilator graphs of commutative rings"],"prefix":"10.1142","volume":"12","author":[{"given":"Sh.","family":"Ebrahimi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran"}]},{"given":"A.","family":"Tehranian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5155-1983","authenticated-orcid":false,"given":"R.","family":"Nikandish","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,8,27]]},"reference":[{"key":"S1793830920500603BIB001","doi-asserted-by":"publisher","DOI":"10.21136\/CMJ.2017.0436-15"},{"key":"S1793830920500603BIB002","doi-asserted-by":"publisher","DOI":"10.4134\/JKMS.2015.52.2.417"},{"key":"S1793830920500603BIB003","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"volume-title":"Introduction to Commutative Algebra","year":"1969","author":"Atiyah M. F.","key":"S1793830920500603BIB004"},{"key":"S1793830920500603BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.707262"},{"key":"S1793830920500603BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"volume-title":"Cohen Macaulay Rings","year":"1997","author":"Bruns W.","key":"S1793830920500603BIB007"},{"volume-title":"Graph Theory","year":"2000","author":"Diestel R.","key":"S1793830920500603BIB008"},{"key":"S1793830920500603BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498816501243"},{"key":"S1793830920500603BIB010","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1498788098"},{"key":"S1793830920500603BIB011","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001","edition":"2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500603","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T07:23:58Z","timestamp":1601623438000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,27]]},"references-count":11,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["10.1142\/S1793830920500603"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500603","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,8,27]]}}}