{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:46Z","timestamp":1740134506963,"version":"3.37.3"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["33?106","9\/112"],"award-info":[{"award-number":["33?106","9\/112"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research","doi-asserted-by":"publisher","award":["33?106","9\/112"],"award-info":[{"award-number":["33?106","9\/112"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>be a near ring. An additive mapping<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>f<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>N<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math>is said to be a right generalized (resp., left generalized) derivation with associated derivation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:math>on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mi>y<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>d<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>(resp.,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>d<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mi>y<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>f<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:math>) for all<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math>. A mapping<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mi>f<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>N<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math>is said to be a generalized derivation with associated derivation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:math>on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>if<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>f<\/mml:mi><\/mml:mrow><\/mml:math>is both a right generalized and a left generalized derivation with associated derivation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:math>on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>. The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.<\/jats:p>","DOI":"10.1155\/2013\/170749","type":"journal-article","created":{"date-parts":[[2013,2,21]],"date-time":"2013-02-21T18:08:19Z","timestamp":1361470099000},"page":"1-5","source":"Crossref","is-referenced-by-count":3,"title":["Generalized Derivations on Prime Near Rings"],"prefix":"10.1155","volume":"2013","author":[{"given":"Asma","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"given":"Howard E.","family":"Bell","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1"}]},{"given":"Phool","family":"Miyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]}],"member":"311","reference":[{"key":"6","doi-asserted-by":"publisher","DOI":"10.1080\/00927879808826190"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/490316"},{"key":"3","series-title":"Mathematical Applications","volume-title":"On derivations in near rings II","volume":"426","year":"1997"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01953371"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72283-7"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1023\/B:AMHU.0000003893.61349.98"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/170749.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/170749.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/170749.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T06:46:14Z","timestamp":1469861174000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/170749\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":6,"alternative-id":["170749","170749"],"URL":"https:\/\/doi.org\/10.1155\/2013\/170749","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2013]]}}}