A note on (alpha)-derivations on semiprime rings

• Autorzy: Thaheem A. , Samman M.
• Języki publikacji: EN

Abstrakty

EN

In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.

Słowa kluczowe

EN

derivation; automorphisms; commuting map; centralizing map; skew derivation; semiprime ring

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 783--788
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Thaheem A.

• Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Mail Box 31261, Dhahran 31261 Saudi Arabia

autor

Samman M.

• Department of Mathematical Sciences King Fahd University of Petroleum and Minerals Mail Box 31261, Dhahran 31261 Saudi Arabia

Bibliografia

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• [2] R. Awtar, On a theorem of Posner, Proc. Cambridge Philos. Soc. 73 (1973), 25-27.
• [3] H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), 92-101.
• [4] M. A. Chaudhry and A. B. Thaheem, A note on automorphisms of prime rings, Demonstratio Math. 29 (1996), 813-816.
• [5] T. C. Chen, Special identities with (α, β)-derivations, Riv. Mat. Univ. Parma 5 (1996), 109-119.
• [6] I. N. Herstein, Rings with Involution, The University of Chicago Press, 1976.
• [7] V. K. Kharchenko and A. Z. Popov, Skew derivations of prime rings, Comm. Algebra 20 (1992), 3321-3345.
• [8] J. Luh, A note on commuting automorphisms of rings, Amer. Math. Monthly 77 (1970), 61-62.
• [9] J. H. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), 113-115.
• [10] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.