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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.13 No.3

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ON (${\sigma},\;{\tau}$)-DERIVATIONS OF PRIME RINGS

On (σ, τ)-Derivations of Prime Rings

한국수학교육학회지시리즈B:순수및응용수학 / 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. (CANAKKALE ONSEKIZ MART UNIVERSITY, FACULTY OF ARTS AND SCIENCES, DEPARTMENT OF MATHEMATICS)
Guven E. (KOCAELI UNIVERSITY, FACULTY OF ARTS AND SCIENCES, DEPARTMENT OF MATHEMATICS)
Soyturk M. (KOCAELI UNIVERSITY, FACULTY OF ARTS AND SCIENCES, DEPARTMENT OF MATHEMATICS)
Kaya K., Guven E., & Soyturk M.. (2006). ON (<TEX>${\sigma},\;{\tau}$</TEX>)-DERIVATIONS OF PRIME RINGS, 13(3), 189-195.

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

한국수학교육학회지시리즈B:순수및응용수학

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