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On Semiprime Rings with (α,α)-Symmetric Derivations
Current Issue
Volume 3, 2015
Issue 4 (August)
Pages: 110-114   |   Vol. 3, No. 4, August 2015   |   Follow on         
Paper in PDF Downloads: 35   Since Aug. 28, 2015 Views: 1720   Since Aug. 28, 2015
Mehsin Jabel Atteya, Al-Mustansiriyah University, College of Education, Department of Mathematics, Baghdad, Iraq.
Dalal Ibraheem Rasen, Al-Mustansiriyah University, College of Education, Department of Mathematics, Baghdad, Iraq.
The main purpose of this paper is to study and investigate concerning a (α,α)-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a (α,α)-symmetric derivations D to satisfy some conditions on R.(i)D([x,y]n+1) =0 for all x, y∈ R. (ii) [D(xn+1),α(y)] = 0 for all x, y ∈R. (iii) [[D(x),α(x)],α(x)]= 0 for all x ∈R. Where α: R → R is an automorphism mapping.
Semiprime Ring, Prime Ring, (α,α)-Derivations, (α,α)-Symmetric Derivation
Ali, Asma, Kumar, Deepak (2006). Ideals and symmetric (σ,σ)-biderivations on prime rings. Aligarh Bull. Math, 25, no. 2, 9-18.
Andima, S. and Pajoohesh, H. (2010). Commutativity of prime rings with derivations. Acta Math. Hungarica,Vol.128 (1-2),1-14.
Ashraf, Mohammad and Nadeem-ur-Rehman(1997/98).On symmetric (σ, σ) – biderivations. Aligarh Bull. Math. 17, 9-16,
Baker, G.A. (1959).A new derivation of Newton’s identities and their applicationto the calculation of the eigenvalues of a matrix, J. Soc. Indust. Appl. Math. 7,143–148.
Bell, H.E. and Daif, M.N. (1995). On derivations and commutativity in prime rings, Acta Math. Hungar. Vol. 66, 337-343.
Bell, H.E .and Martindale, W.S. (1987). Centralizing mappings of semiprimerings, Canad. Math. Bull.30(1), 92-101.
Breˇsar, M.(1992).On composition of (α, β) derivations of rings and applied to von Neumen algebras, Acta. Sci. Math, 369-376.
Breˇsar, M.(1993).Centralizing mappings and derivations in prime rings. J. Algebra156, 385-394.
Breˇsar, M. and Vukman, J. (1989). On some additive mappings in rings with involution. Aequations Math., 38, 178-185.
Çeven, Yilmaz and Öztürk, Mehmet Ali (2007). Some properties of symmetric bi-(,τ)-derivations in near-rings. Commun. Korean Math. Soc. 22, No. 4, 487-491.
Da Providencia, Joao (1994). The numerical ranges of derivations and quantum physics. Special Issue: The numerical range and numerical radius. Linear and Multilinear Algebra 37, no. 1-3, 213–220.
Herstein, I. N. (1978). A note on derivations, Canad. Math. Bull, 21, 369-370.
Javed ,M. A., Zeeshan, M. Aslam and Nadeem ,M. (2012). A note on (α, α)-symmetric derivations in semiprime rings. International Journal of Algebra, Vol. 6, no.16,757-767.
Lee, T.K. (2001). α-commuting mappings in semiprime rings. Communicationsin Algebra, (29), 2945 - 2951.
Pajoohesh, H. (2007). Positive derivations on lattice ordered rings of Matrices. Quaestiones Mathematicae, Vol. 30, 275-284.
Park, Kyoo-Hong (2009). On prime and semiprime rings with symmetric n-derivations. Journal of The Chungcheong Mathematical Society,Vol.22, No. 3, 451-458.
Samman, M., and Alyamani, N. (2007), Derivations and reverse derivations in semiprimerings, International Mathematical Forum, 2, no.39,1895-1902.
Shu-hua, Z. and Feng-wen, N. (2002). Derivations on semiprime rings. Journal of Mathematical Research and Exposition, Vol.22,No.3,371-374.
Thaheem, A.B. and Samman, M.S.(2001).A Note on derivations on semiprimerings. Demonstratio Math.,34,783-788.
Vukman, J. (1989). Symmetric bi-derivations on prime and semiprime rings. Aequationes Math. 38 ,245-254.
Vukman, J. (1995). Derivations on semiprime rings. Bull. Austral. Math. Soc., 53,353-359.
Wu, Rui Hua, Zhang, Jian Hua(2006).Properties of Jordan (α,α)-derivations on semiprime rings. (Chinese) J. Shaanxi Normal Univ. Nat. Sci. Ed. 34, no. 2,119-120.
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