Some results on ?-ideal of ?-prime ring
Some results on ?-ideal of ?-prime ring
Let R be a ?-prime ring with characteristic not 2, Z(R) be the center ofR, I be a nonzero ?-ideal of R, ?, ? : R -> R be two automorphisms, dbe a nonzero (?, ?)-derivation of R and h be a nonzero derivation of R.In the present paper, it is shown that (i) If d (I) ? C?,?and ? commuteswith ? then R is commutative. (ii) Let ? and ? commute with ?. Ifa ? I ? S?(R) and [d(I), a]and h commute with ?. If dh (I) ? C?,?and h (I) ? I then R is? C commutative.
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- Aydın N., Kaya K.: Some Generalizations in Prime Rings with (?, ? )-Derivation, Doğa-Tr. J. Mathematics, vol 16 (1992) 169 - 176.
- Herstein I. N. : A Note on Derivation II, Canad. Math. Bull., 22, 4, (1979) 509 - 511.
- Kaya K. : (?, ? )-Türevli Asal Halkalar Üzerine, Doğa-Tr. J. Mathematics, (1988) 42 - 45.
- Oukhtite L., Salhi S.: On Commutativity of ?-Prime Rings, Glasnik Matematicki, vol. 41 no. 1 (2006) 57 - 64.
- Oukhtite L., Salhi S.: Derivations and Commutativity of ?-Prime Rings, Int. J. Contemp. Sci., vol. 1 no. 9 (2006) 439 - 448.
- Oukhtite L., Salhi S.: ?-Prime Rings with a special kind of automorphism, Int. J. Contemp. Math. Sci., vol. 2 no. 3 (2007) 127 - 133.
- Posner E. : Derivations in Prime Rings, Proc. Amer. Math. Soc., 8, (1957).
- Shuliang H.: Some Generalizations in Certain Classes of Rings with Involution, Bol. Soc. Paran. Mat., 29, 1, (2011) 9 - 16.
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi