{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T07:40:22Z","timestamp":1775893222133,"version":"3.50.1"},"reference-count":9,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2015]]},"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 generalized semiderivation on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>if there exists a semiderivation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>d<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>N<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math>associated with a function<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>g<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>N<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math>such that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>g<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mi>g<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>+<\/mml:mo><mml:mi>x<\/mml:mi><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>g<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mi>g<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>for all<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><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>. In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2015\/867923","type":"journal-article","created":{"date-parts":[[2015,11,8]],"date-time":"2015-11-08T16:01:58Z","timestamp":1446998518000},"page":"1-7","source":"Crossref","is-referenced-by-count":3,"title":["On Generalized Semiderivations of Prime Near Rings"],"prefix":"10.1155","volume":"2015","author":[{"given":"Abdelkarim","family":"Boua","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences of Agadir, Ibn Zohr University, P.O. Box 8106, Agadir, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Raji","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences et Techniques, Universit\u00e9 Moulay Isma\u00efl, Groupe d\u2019Alg\u00e8bre et Applications, BP 509, Boutalamine, Errachidia, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asma","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farhat","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"6","doi-asserted-by":"publisher","DOI":"10.4153\/cmb-1983-042-2"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72283-7"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1142\/s1793557113500435"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.4153\/cmb-1978-065-x"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1481-0_10"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/490316"},{"issue":"3","key":"8","first-page":"325","volume":"37","year":"2013","journal-title":"Southeast Asian Bulletin of Mathematics"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/bf01953371"},{"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\/2015\/867923.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2015\/867923.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2015\/867923.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T23:17:37Z","timestamp":1471562257000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2015\/867923\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":9,"alternative-id":["867923","867923"],"URL":"https:\/\/doi.org\/10.1155\/2015\/867923","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}