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ISSN : 1226-0657

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Vol.25 No.3
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A REMARK ON GENERALIZED DERIVATIONS IN RINGS AND ALGEBRAS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2018, v.25 no.3, pp.181-191
https://doi.org/10.7468/jksmeb.2018.25.3.181
Rehman, Nadeem Ur
Rehman,, N. U. (2018). A REMARK ON GENERALIZED DERIVATIONS IN RINGS AND ALGEBRAS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(3), 181-191, https://doi.org/10.7468/jksmeb.2018.25.3.181
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Abstract

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying <TEX>$(G([x,y</TEX><TEX>]</TEX><TEX>)-[G(x),y</TEX><TEX>]</TEX><TEX>)^n=0$</TEX> for all x, <TEX>$y{\in}I$</TEX>, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

keywords
generalized derivations, generalized polynomial identity (GPI)

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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