{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T15:13:38Z","timestamp":1770909218359,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"DST, India","award":["INSPIRE programme (IF160175)"],"award-info":[{"award-number":["INSPIRE programme (IF160175)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p>Let [Formula: see text] be a commutative ring with identity and [Formula: see text], a fixed integer. Let [Formula: see text] be the set of all [Formula: see text]-maximal elements in [Formula: see text] Associate a [Formula: see text]-maximal hypergraph [Formula: see text] to [Formula: see text] with vertex set [Formula: see text] and for distinct elements [Formula: see text] in [Formula: see text], the set [Formula: see text] is an edge of [Formula: see text] if and only if [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we determine all isomorphism classes of finite commutative non-local rings with identity whose [Formula: see text]-maximal hypergraph has genus one. Finally, we classify all finite commutative non-local rings [Formula: see text] for which [Formula: see text] is projective.<\/jats:p>","DOI":"10.1142\/s1793830919500101","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T08:46:00Z","timestamp":1543394760000},"page":"1950010","source":"Crossref","is-referenced-by-count":2,"title":["On the genus of the k-maximal hypergraph of commutative rings"],"prefix":"10.1142","volume":"11","author":[{"given":"K.","family":"Selvakumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu 627 012, India"}]},{"given":"V. C.","family":"Amritha","sequence":"additional","affiliation":[{"name":"Research Scholar, Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu 627 012, India"}]}],"member":"219","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"S1793830919500101BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s10468-011-9309-z"},{"key":"S1793830919500101BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S1793830919500101BIB003","doi-asserted-by":"publisher","DOI":"10.3906\/mat-1505-23"},{"key":"S1793830919500101BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"S1793830919500101BIB005","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"2003"},{"key":"S1793830919500101BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608704"},{"key":"S1793830919500101BIB007","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"S1793830919500101BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.akcej.2015.11.011"},{"issue":"4","key":"S1793830919500101BIB009","first-page":"9","volume":"5","author":"Dorbidi H. 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