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Abstrakty
We show that if α and β are centralizing automorphisms and d a centralizing (α, β)-derivation of a semiprime ring R, then d is commuting. Some results on α-derivations and centralizing derivations of semiprime rings follow as applications of this result.
Słowa kluczowe
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Czasopismo
Rocznik
Tom
Strony
283--287
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
autor
- Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Bibliografia
- [1] R. Awtar, On a theorem of Posner, Proc. Cambridge Philos. Soc. 73 (1973), 25-27.
- [2] H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), 92-101.
- [3] M. Brešar, Centralizing mappings on von Neumann algebras, Proc. Amer. Math. Soc. Ill (1991), 501-510.
- [4] M. Brešar, On a generalization of the notion of centralizing mappings, Proc. Amer. Math. Soc. 114 (1992), 641-649.
- [5] M. Brešar, On the composition of (α, β)-derivation of rings, and application to von Neumann algebras, Acta Sci. Math. (1992), 369-376.
- [6] M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.
- [7] T. C. Chen, Special identities with (α, β-derivations, Riv. Mat. Univ. Parma 5 (1996), 109-119.
- [8] N. Jacobson, Structure of rings, Colloq. Publ. 37, Amer. Math. Soc. (1956).
- [9] V. K. Kharchenko and A. Z. Popov, Skew derivations of prime rings, Comm. Algebra 20 (1992), 3321-3345.
- [10] J. Luh, A note on commuting automorphisms of rings, Amer. Math. Monthly 77 (1970), 61-62.
- [11] J. H. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. 19 (1976), 113-15.
- [12] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
- [13] A. B. Thaheem and M. S. Samman, A note on a-derivations on semiprime rings, Demonstratio Math. 34 (2001), 783-788.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0007-0003