{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:09:40Z","timestamp":1746803380870,"version":"3.40.5"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100008536","name":"Lanzhou University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008536","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E2\"><mml:mi>R<\/mml:mi><\/mml:math>be a ring and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E3\"><mml:mi>M<\/mml:mi><\/mml:math>a right<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E4\"><mml:mi>R<\/mml:mi><\/mml:math>-module. In this note, we show that a quotient of an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E5\"><mml:mo>\u2295<\/mml:mo><\/mml:math>-cofinitely supplemented module is not in general<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E6\"><mml:mo>\u2295<\/mml:mo><\/mml:math>-cofinitely supplemented and prove that if a module<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E7\"><mml:mi>M<\/mml:mi><\/mml:math>is an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E8\"><mml:mo>\u2295<\/mml:mo><\/mml:math>-cofinitely supplemented multiplication module with Rad<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E9\"><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>\u226a<\/mml:mo><mml:mi>M<\/mml:mi><\/mml:math>, then<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E10\"><mml:mi>M<\/mml:mi><\/mml:math>can be written as an irredundant sum of local direct summand of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E11\"><mml:mi>M<\/mml:mi><\/mml:math>. An extension of the result of Calisici and Pancar [1], here it is shown that an arbitrary module is cofinitely semiperfect if and only if it is an (amply) cofinitely supplemented by supplements which have projective covers.<\/jats:p>","DOI":"10.1155\/2007\/10836","type":"journal-article","created":{"date-parts":[[2007,6,28]],"date-time":"2007-06-28T12:27:49Z","timestamp":1183033669000},"page":"1-5","source":"Crossref","is-referenced-by-count":2,"title":["A Note on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E1\"><mml:mo>\u2295<\/mml:mo><\/mml:math>-Cofinitely Supplemented Modules"],"prefix":"10.1155","volume":"2007","author":[{"given":"Yongduo","family":"Wang","sequence":"first","affiliation":[]},{"given":"Qing","family":"Sun","sequence":"additional","affiliation":[]}],"member":"311","reference":[{"issue":"2","key":"1","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s11202-005-0037-7","volume":"46","year":"2005","journal-title":"Siberian Mathematical Journal"},{"issue":"4","key":"2","first-page":"1083","volume":"54(129)","year":"2004","journal-title":"Czechoslovak Mathematical Journal"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.2307\/2036549"},{"key":"4","series-title":"Lecture Notes in Pure and Applied Mathematics","first-page":"149","volume-title":"A dual notion of CS-modules generalization","volume":"208","year":"2000"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1155\/S016117120320346X"},{"issue":"4","key":"6","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1080\/00927878808823601","volume":"16","year":"1988","journal-title":"Communications in Algebra"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/010836.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/010836.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T17:23:21Z","timestamp":1588785801000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2007\/010836\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":6,"alternative-id":["010836","10836"],"URL":"https:\/\/doi.org\/10.1155\/2007\/10836","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2007]]}}}