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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 2, Pages 345–351
(Mi smj969)
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This article is cited in 4 scientific papers (total in 4 papers)
Some properties of prime near-rings with $(\sigma,\tau)$-derivation
Ö. Gölbaşi Cumhuriyet University
Abstract:
Some results by Bell and Mason on commutativity in near-rings are generalized. Let $N$ be a prime right near-ring with multiplicative center $Z$ and let $D$ be a $(\sigma,\tau)$-derivation on $N$ such that $\sigma D=D\sigma$ and $\tau D=D\tau$. The following results are proved: (i) If $D(N)\subset Z$ or $[D(N),D(N)]=0$ or $[D(N),D(N)]_{\sigma,\tau}=0$ then $(N,+)$ is abelian; (ii) If $D(xy)=D(x)D(y)$ or $D(xy)=D(y)D(x)$ for all $x,y\in N$ then $D=0$.
Keywords:
prime near-ring, derivation, $(\sigma,\tau)$-derivation.
Received: 07.04.2003
Citation:
Ö. Gölbaşi, “Some properties of prime near-rings with $(\sigma,\tau)$-derivation”, Sibirsk. Mat. Zh., 46:2 (2005), 345–351; Siberian Math. J., 46:2 (2005), 270–275
Linking options:
https://www.mathnet.ru/eng/smj969 https://www.mathnet.ru/eng/smj/v46/i2/p345
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Abstract page: | 372 | Full-text PDF : | 109 | References: | 51 |
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