On alfa-derivations of prime and semiprime rings

Vukman, J.

Artykuł - szczegóły

Tytuł artykułu

On alfa-derivations of prime and semiprime rings

Autorzy

Vukman J.

Wybrane pełne teksty z tego czasopisma

http://www.degruyter.com/view/j/dema

Identyfikatory

Warianty tytułu

Języki publikacji

Abstrakty

In this paper we investigate identities with alfa-derivations on prime and semiprime rings. We prove, for example, the following result. If D : R - R is an alfa-derivation of a 2 and 3-torsion free semiprime ring R such that [D(x},x2] = 0 holds, for all x is an element of R, then D maps R into its center. The results of this paper are motivated by the work of Thaheem and Samman [20].

Słowa kluczowe

automorphism prime ring semiprime ring derivation commuting mappings centralizing mapping

pierścienie pierwsze półpierścienie automorfizm odwzorowania pochodne

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2005

Tom

Vol. 38, nr 2

Strony

283--290

Opis fizyczny

Bibliogr. 22 poz.

Twórcy

autor

Vukman J.

joso.vukman@uni-mb.si

Department of Mathematics, University of Maribor, PEF, Koroska 160, 2000 Maribor, Slovenia

Bibliografia

[1] K. I. Beidar, W. S. Martindale III, A. V. Mikhalev, Rings with Generalized Identities, Marcel Dekker, Inc. New York 1996.
[2] M. Brešar, J. Vukman, Orthogonal derivations and an extension of a theorem of Posner, Radovi Mat. Vol. 5 (1989), 237-246.
[3] M. Brešar, J. Vukman, Jordan (ϑ, ϕ)-derivations, Glasnik Mat. 26 (1991), 13-17.
[4] M. Brešar, On the composition of (α, β)-derivations of rings, and an application to von Neumann algebras, Acta Sci. Math. (1992), 369-376.
[5] M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.
[6] M. Brešar, On skew-commuting mappings of rings, Bull, Austral. Math. Soc. 47 (1993), 291-296.
[7] M. Brešar, B. Hvala, On additive maps of prime rings, Bull. Austral. Math. Soc. Vol. 51 (1995), 377-381.
[8] J. C. Chang, α-derivations with invertible values, Bull. Inst. Math. Acad. Sinica, Vol. 13 (1985), 323-333 .
[9] J. C. Chang, On fixed power central (α, β)-derivations, Bull. Inst. Math. Acad. Sinica, Vol. 15 (1987), 163-178.
[10] J. C. Chang, A note on (α, β)-derivations , Chinese J. Math. Vol. 19 (1991), 277-285.
[11] J. C. Chang, On (α, β)-derivations of prime rings, Chinese J. Math. Vol. 22 (1994), 21-30.
[12] M. A. Chaudhry, A. B. Thaheem, (α, β)-derivations on semiprime rings, Intern. Math. Journal, Vol. 3 (2003), 1033-1042.
[13] M. A. Chaudhry, A. B. Thaheem, On (α, β)-derivations of semiprime rings, Demonstratio Math. Vol. 36, 2 (2003), 283-287.
[14] T. C. Chen, Special identities with (α, β)-derivations, Riv. Mat. Univ. Parma 5 (1996), 109-119.
[15] L. O. Chung, J. Luh, Semiprime rings with nilpotent derivatives, Canad. Math. Bull. 24 (1981), 415-421.
[16] I. N. Divinsky, On commuting automorphisms of rings, Trans. Ray. Canada Sect. III, 49 (1955), 19-22.
[17] J. Luh, A note on commuting automorphisms of rings, Amer. Math. Monthly 77 (1970), 61-62.
[18] J. H. Mayne, Centralizing automorphisms of prime rings, Canad. Math. Bull. Vol. 19 (1976), 113-115.
[19] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
[20] A. B. Thaheem, M. S. Samman, A note on a-derivations on semiprime rings, Demonstratio Math. Vol. 34, 4 (2001), 783-788.
[21] J. Vukman, Derivations on semiprime rings, Bull. Austral. Math. Soc. 53 (1995), 353-359.
[22] J. Vukman, Centralizers on semiprime rings, Comment. Math. Univ. Carolinae 42 (2001), 783-788.

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-article-PWA3-0013-0003