On a Theorem of Posner for 3-Prime Near-Rings with (s, t) - Derivation

Yıl 2007, Cilt: 36 Sayı: 1, 43 - 47, 01.01.2007

Ö. Gölbaşı

Öz

The analog of Posner’s theorem on the composition of two derivations in prime rings is proved for 3–prime near-rings with d1 a (σ, τ )–derivation and d2 a derivation.

Anahtar Kelimeler

3–prime near-rings, Commutativity, 2000 AMS Classification: 16 Y 30

Kaynakça

• Beidar, K. I., Fong, Y. and Wang, X. K. Posner and Herstein Theorems for derivations of 3–prime near-rings, Communications in Algebra 24 (5), 1581–1589, 1996.
• Bell, H. E. and Arga¸c, N. Derivations, products of derivations and commutativity in near- rings, Algebra Colloquium 8 4, 399–407, 2001.
• Bell, H. E. and Mason G. On Derivations in Near-rings, Near-rings and Near-fields (North- Holland Mathematical Studies 137, 1987).
• G¨olba¸sı, ¨O. and Aydın, N. Results on prime near-rings with (σ, τ )–derivation, Mathematical Journal of Okayama University 46, 1–7, 2004.
• Pilz, G. Near-rings, 2nd Ed. (North Holland, Amsterdam, 1983).
• Posner, E. C. Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093–1100, 1957.