{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T12:34:19Z","timestamp":1773405259210,"version":"3.50.1"},"reference-count":8,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"MOHE","award":["01-12-10-978FR"],"award-info":[{"award-number":["01-12-10-978FR"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>M<\/mml:mi><\/mml:math>be a 2-torsion-free semiprime<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u0393<\/mml:mi><\/mml:math>-ring satisfying the condition<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>a<\/mml:mi><mml:mi>\u03b1<\/mml:mi><mml:mi>b<\/mml:mi><mml:mi>\u03b2<\/mml:mi><mml:mi>c<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>a<\/mml:mi><mml:mi>\u03b2<\/mml:mi><mml:mi>b<\/mml:mi><mml:mi>\u03b1<\/mml:mi><mml:mi>c<\/mml:mi><\/mml:mrow><\/mml:math>for all<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>a<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>b<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo>,\u2009\u2009<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>\u03b2<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>\u0393<\/mml:mi><\/mml:math>, and let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>M<\/mml:mi><\/mml:math>be an additive mapping such that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>\u03b1<\/mml:mi><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>D<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mi>x<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>\u03b1<\/mml:mi><mml:mi>d<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:math>for all<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>x<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo>,\u2009\u2009<\/mml:mo><mml:mi>\u03b1<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>\u0393<\/mml:mi><\/mml:math>and for some derivation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>d<\/mml:mi><\/mml:math>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>M<\/mml:mi><\/mml:math>. We prove that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>D<\/mml:mi><\/mml:math>is a generalized derivation.<\/jats:p>","DOI":"10.1155\/2012\/270132","type":"journal-article","created":{"date-parts":[[2012,2,16]],"date-time":"2012-02-16T21:01:28Z","timestamp":1329426088000},"page":"1-14","source":"Crossref","is-referenced-by-count":3,"title":["Generalized Derivations in Semiprime Gamma Rings"],"prefix":"10.1155","volume":"2012","author":[{"given":"Kalyan Kumar","family":"Dey","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh"}]},{"given":"Akhil Chandra","family":"Paul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh"}]},{"given":"Isamiddin S.","family":"Rakhimov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, FS, and Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Malaysia"}]}],"member":"98","reference":[{"key":"9","doi-asserted-by":"publisher","DOI":"10.1080\/00927879808826190"},{"issue":"29\u201332","key":"8","first-page":"1481","volume":"2","year":"2007","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"issue":"1\u20134","key":"3","first-page":"17","volume":"5","year":"2011","journal-title":"International Journal of Algebra"},{"key":"6","first-page":"11","volume":"33","year":"2004","journal-title":"Hacettepe Journal of Mathematics and Statistics"},{"issue":"13\u201316","key":"1","first-page":"677","volume":"4","year":"2010","journal-title":"International Journal of Algebra"},{"issue":"9\u201312","key":"4","first-page":"591","volume":"4","year":"2010","journal-title":"International Journal of Algebra"},{"key":"15","first-page":"43","volume":"44","year":"2002","journal-title":"Mathematical Journal of Okayama University"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.3336\/gm.39.1.03"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/270132.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/270132.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/270132.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T18:10:17Z","timestamp":1470161417000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/270132\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":8,"alternative-id":["270132","270132"],"URL":"https:\/\/doi.org\/10.1155\/2012\/270132","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}