On (σ, τ)-Derivations of Prime Rings

Kaya K.; Kaya K.; Guven E.; Guven E.; Soyturk M.; Soyturk M.

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P-ISSN3059-0604
E-ISSN3059-1309
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Vol.13 No.3

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On (σ, τ)-Derivations of Prime Rings

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2006, v.13 no.3, pp.189-195

Kaya K.
Guven E.
Soyturk M.

Kaya, K. , Guven, E. , & Soyturk, M. (2006). On (σ, τ)-Derivations of Prime Rings, 13(3), 189-195.

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Abstract

Let R be a prime ring with characteristics not 2 and ${\sigma},\;{\tau},\;{\alpha},\;{\beta}$ be auto-morphisms of R. Suppose that $d_1$ is a (${\sigma},\;{\tau}$)-derivation and $d_2$ is a (${\alpha},\;{\beta}$)-derivation on R such that $d_{2}{\alpha}\;=\;{\alpha}d_2,\;d_2{\beta}\;=\;{\beta}d_2$. In this note it is shown that; (1) If $d_1d_2$(R) = 0 then $d_1$ = 0 or $d_2$ = 0. (2) If [$d_1(R),d_2(R)$] = 0 then R is commutative. (3) If($d_1(R),d_2(R)$) = 0 then R is commutative. (4) If $[d_1(R),d_2(R)]_{\sigma,\tau}$ = 0 then R is commutative.

keywords: prime ring, (&lt, TEX&gt, ${\sigma}, \, {\tau}$&lt, /TEX&gt, )-derivation, (&lt, TEX&gt, ${\sigma}, \, {\tau}$&lt, /TEX&gt, )-Lie ideal

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Article Contents

Vol.13 No.3

On (σ, τ)-Derivations of Prime Rings

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics