{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:38:31Z","timestamp":1740155911071,"version":"3.37.3"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with identity which is not an integral domain. An ideal [Formula: see text] of a ring [Formula: see text] is called an annihilating ideal if there exists [Formula: see text] such that [Formula: see text]. Let [Formula: see text] be a simple undirect graph associated with [Formula: see text] whose vertex set is the set of all nonzero annihilating ideals of [Formula: see text] and two distinct vertices [Formula: see text] are joined if and only if [Formula: see text] is also an annihilating ideal of [Formula: see text]. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. In this paper, we characterize all rings whose [Formula: see text] is perfect. <\/jats:p>","DOI":"10.1142\/s1793830918500477","type":"journal-article","created":{"date-parts":[[2018,4,23]],"date-time":"2018-04-23T04:30:10Z","timestamp":1524457810000},"page":"1850047","source":"Crossref","is-referenced-by-count":2,"title":["Perfectness of a graph associated with annihilating ideals of a ring"],"prefix":"10.1142","volume":"10","author":[{"given":"V.","family":"Aghapouramin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University of Karaj, Karaj, Iran"},{"name":"Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6912-3955","authenticated-orcid":false,"given":"M. J.","family":"Nikmehr","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University of Karaj, Karaj, Iran"},{"name":"Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,7,30]]},"reference":[{"doi-asserted-by":"publisher","key":"S1793830918500477BIB001","DOI":"10.1006\/jabr.1998.7840"},{"volume-title":"Introduction to Commutative Algebra","year":"1969","author":"Atiyah M. F.","key":"S1793830918500477BIB002"},{"doi-asserted-by":"publisher","key":"S1793830918500477BIB003","DOI":"10.1080\/00927872.2012.707262"},{"doi-asserted-by":"publisher","key":"S1793830918500477BIB004","DOI":"10.1080\/00927872.2014.897188"},{"doi-asserted-by":"publisher","key":"S1793830918500477BIB005","DOI":"10.1016\/0021-8693(88)90202-5"},{"volume-title":"Cohen\u2013Macaulay Rings","year":"1997","author":"Bruns W.","key":"S1793830918500477BIB006"},{"volume-title":"Graph Theory","year":"2000","author":"Diestel R.","key":"S1793830918500477BIB007"},{"doi-asserted-by":"publisher","key":"S1793830918500477BIB008","DOI":"10.1142\/S0219498816501243"},{"doi-asserted-by":"publisher","key":"S1793830918500477BIB009","DOI":"10.7151\/dmgaa.1241"},{"issue":"4","key":"S1793830918500477BIB010","first-page":"22","volume":"6","author":"Visweswaram S.","year":"2014","journal-title":"Discrete Math. Algorithms Appl."},{"key":"S1793830918500477BIB011","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001","edition":"2"},{"volume-title":"Foundations of Module and Ring Theory","year":"1991","author":"Wisbauer R.","key":"S1793830918500477BIB012"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830918500477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:44:45Z","timestamp":1565081085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830918500477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,30]]},"references-count":12,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2018,7,30]]},"published-print":{"date-parts":[[2018,8]]}},"alternative-id":["10.1142\/S1793830918500477"],"URL":"https:\/\/doi.org\/10.1142\/s1793830918500477","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2018,7,30]]}}}