{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,12]],"date-time":"2024-08-12T00:05:01Z","timestamp":1723421101773},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p>Let [Formula: see text] be a commutative ring with identity. The co-annihilating-ideal graph of [Formula: see text], denoted by [Formula: see text], is a graph whose vertex set is the set of all nonzero proper ideals of R and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text]. In this paper, we study the planarity and genus of [Formula: see text]. In particular, we characterize all Artinian rings [Formula: see text] for which the genus of [Formula: see text] is zero or one.<\/jats:p>","DOI":"10.1142\/s1793830921500063","type":"journal-article","created":{"date-parts":[[2020,8,16]],"date-time":"2020-08-16T10:14:49Z","timestamp":1597572889000},"page":"2150006","source":"Crossref","is-referenced-by-count":0,"title":["Classification of rings with toroidal co-annihilating-ideal graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"Rana","family":"Khoeilar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran"}]},{"given":"Jafar","family":"Amjadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"S1793830921500063BIB001","doi-asserted-by":"crossref","first-page":"3","DOI":"10.4153\/CMB-2016-017-1","volume":"60","author":"Akbari S.","year":"2017","journal-title":"Canad. Math. Bull."},{"key":"S1793830921500063BIB002","first-page":"117","volume":"1","author":"Alilou A.","year":"2016","journal-title":"Commun. Comb. Optim."},{"key":"S1793830921500063BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830916500294"},{"key":"S1793830921500063BIB004","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1080\/00927872.2012.753606","volume":"42","author":"Aliniaeifard F.","year":"2014","journal-title":"Comm. Algebra"},{"key":"S1793830921500063BIB005","doi-asserted-by":"crossref","first-page":"3073","DOI":"10.1080\/00927870802110888","volume":"36","author":"Anderson D. F.","year":"2008","journal-title":"Comm. Algebra"},{"issue":"320","key":"S1793830921500063BIB006","doi-asserted-by":"crossref","first-page":"2706","DOI":"10.1016\/j.jalgebra.2008.06.028","volume":"26","author":"Anderson D. F.","year":"2008","journal-title":"J. Algebra"},{"key":"S1793830921500063BIB007","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1006\/jabr.1998.7840","volume":"217","author":"Anderson D. F.","year":"1999","journal-title":"J. Algebra"},{"key":"S1793830921500063BIB008","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/0021-8693(88)90202-5","volume":"116","author":"Beck I.","year":"1988","journal-title":"J. Algebra"},{"key":"S1793830921500063BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004896"},{"key":"S1793830921500063BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004902"},{"key":"S1793830921500063BIB011","doi-asserted-by":"crossref","first-page":"271","DOI":"10.4064\/fm-15-1-271-283","volume":"15","author":"Kuratowski K.","year":"1930","journal-title":"Fund. Math."},{"key":"S1793830921500063BIB012","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.jalgebra.2006.01.019","volume":"301","author":"Lucas T. G.","year":"2006","journal-title":"J. Algebra"},{"key":"S1793830921500063BIB013","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1016\/j.jalgebra.2007.02.003","volume":"319","author":"Maimani H. R.","year":"2008","journal-title":"J. Algebra"},{"volume-title":"Algebraic Topology: An Introduction","year":"1967","author":"Massey W.","key":"S1793830921500063BIB014"},{"key":"S1793830921500063BIB015","first-page":"203","volume":"1","author":"Redmond S. P.","year":"2002","journal-title":"Int. J. Comm. Ring"},{"key":"S1793830921500063BIB016","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1080\/00927872.2016.1206344","volume":"45","author":"Selvakumar K.","year":"2017","journal-title":"Comm. Algebra"},{"key":"S1793830921500063BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830917500586"},{"key":"S1793830921500063BIB018","doi-asserted-by":"crossref","first-page":"1527","DOI":"10.1515\/ms-2016-0241","volume":"66","author":"Shariatinia A.","year":"2016","journal-title":"Math. Slovaca"},{"key":"S1793830921500063BIB019","first-page":"147","volume":"8","author":"Chelvam T. Tamizh","year":"2013","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"S1793830921500063BIB020","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ajmsc.2016.09.004","volume":"23","author":"Chelvman T. Tamizh","year":"2017","journal-title":"Arab J. Math. Sci."},{"key":"S1793830921500063BIB021","first-page":"19","volume":"2","author":"Visweswaran S.","year":"2017","journal-title":"Commun. Comb. Optim."},{"key":"S1793830921500063BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830914500475"},{"key":"S1793830921500063BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830916500439"},{"key":"S1793830921500063BIB024","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s40863-017-0065-9","volume":"11","author":"Visweswaran S.","year":"2017","journal-title":"S\u00e3o Paulo J. Math. Sci."},{"key":"S1793830921500063BIB025","first-page":"280","volume":"2","author":"Wagner K.","year":"1937","journal-title":"Deutsche Math."},{"key":"S1793830921500063BIB026","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001","edition":"2"},{"volume-title":"Graphs, Groups and Surfaces","year":"1973","author":"White A. T.","key":"S1793830921500063BIB027"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500063","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T22:09:51Z","timestamp":1723414191000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500063"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,21]]},"references-count":27,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10.1142\/S1793830921500063"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500063","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,9,21]]}}}