Abstract
References
- Ashraf, M. ve Rehman, N. (2001). On derivations and commutativity in prime rings: East-West J. of Math., 3 (1), 87-91.
- Ashraf, M., Asma, A. ve Shakir, A. (2007). Some commutativity theorems for rings generalized derivations: Southeast Asian Bulletin of Math., 31, 415-421.
- Bell, H. E., Martindale III, W. S., (1988). On semi-derivations and commutativity in prime rings: Canadian Math. Bull., 31.(4), 500-508.
- Bell, H. E. and Kappe, L. C. (1989). Rings in which derivations satisfy certain algebraic conditions: Acta Math. Hungarica, 53, 339-346.
- Bergen, J., (1983). Derivations in prime rings: Canadian Math. Bull., 26 (3), 267-270.
- Brešar, M.,Vukman, J., (1989). Orthogonal derivation and an extension of a theorem of Posner: Rad. Mat.5, no. 2, 237–246.
- Bresar, M., (1990). Semi-derivations of prime rings: Proc. Amer. Math. Soc., 108 (4), 859-860.
- Chang, J. C., (1984). On semi-derivations of prime rings: Chinese Journal Mathematics, 12(4), 255- 262.
- Nabiel, H., (2013). Semiderivations and commutativity in semiprime rings: Gen. Math. Notes, Vol. 19, No. 2, 71-82.
- Posner, E.C.,(1957). Derivations in prime rings: Proc. Amer. Math. Soc., 8, 1093-1100.
Abstract
Özet. Bu makalede, " bir torsion free yarı-asal halka, ve örten fonksiyonu ile belirlenmiş sıfırdan farklı iki yarı-türev olmak üzere ve ın ortogonal olması için gerek ve yeter koşul i) ii) iii) her için iv) fonksiyonu ile belirlenmiş bir yarı-türevdir, koşullarından herhangi birinin sağlanmasıdır" ve ayrıca "her için i) , ii) , iii) koşullarından birini sağlayan halkası sıfırdan farklı bir merkezil ideal kapsar" teoremleri gösterilmiştir.
Anahtar Kelimeler: Yarı-türevler, ortogonal türevler, yarı-asal halkalar
Abstract. In this paper, it is shown that if is torsion free semiprime ring, and are semiderivations associated with a surjective function of , and are orthogonal semiderivations if and only if the following conditions are satisfied i) ii) iii) , iv) is a semiderivation associated with a function. Also, it is proved that if i) , ii) , iii) conditions are satisfied for all then contains a nonzero central ideal.
Keywords: Semi-derivations, orthogonal derivations, semi-prime rings
References
- Ashraf, M. ve Rehman, N. (2001). On derivations and commutativity in prime rings: East-West J. of Math., 3 (1), 87-91.
- Ashraf, M., Asma, A. ve Shakir, A. (2007). Some commutativity theorems for rings generalized derivations: Southeast Asian Bulletin of Math., 31, 415-421.
- Bell, H. E., Martindale III, W. S., (1988). On semi-derivations and commutativity in prime rings: Canadian Math. Bull., 31.(4), 500-508.
- Bell, H. E. and Kappe, L. C. (1989). Rings in which derivations satisfy certain algebraic conditions: Acta Math. Hungarica, 53, 339-346.
- Bergen, J., (1983). Derivations in prime rings: Canadian Math. Bull., 26 (3), 267-270.
- Brešar, M.,Vukman, J., (1989). Orthogonal derivation and an extension of a theorem of Posner: Rad. Mat.5, no. 2, 237–246.
- Bresar, M., (1990). Semi-derivations of prime rings: Proc. Amer. Math. Soc., 108 (4), 859-860.
- Chang, J. C., (1984). On semi-derivations of prime rings: Chinese Journal Mathematics, 12(4), 255- 262.
- Nabiel, H., (2013). Semiderivations and commutativity in semiprime rings: Gen. Math. Notes, Vol. 19, No. 2, 71-82.
- Posner, E.C.,(1957). Derivations in prime rings: Proc. Amer. Math. Soc., 8, 1093-1100.
Details
| Journal Section | Natural Sciences Research Article |
|---|---|
| Authors | |
| Publication Date | April 6, 2016 |
| Published in Issue | Year 2016 Volume: 37 Issue: 2 |