Identities with two automorphisms on semiprime rings

• Autorzy: Kosi-Ulbl I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate identities with two automorphisms on semiprime rings. We prove the following result: Let T, S : R approaches R be automorphisms where R is a 2-torsion free semiprime ring satisfying the relation T(x)x = xS(x) for all x is an element of R. In this case the mapping x approaches T(x) - x maps R into its center and T = S.

Słowa kluczowe

EN

automorphism; prime ring; semiprime ring; derivation; commuting ring; skew-centralizing mapping

PL

automorfizm; pierścienie; odwzorowania; odwzorowania pochodne; półpierścienie

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 1
• Strony: 37--42
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kosi-Ulbl I.

• 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, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385–394.
• [3] M. Brešar, On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), 291–296.
• [4] M. Brešar, On generalized biderivations and related maps, J. Algebra 172 (1995), 764–786.
• [5] M. Brešar, B. Hvala, On additive maps of prime rings, Bull. Austral. Math. Soc. 51 (1995), 377–381.
• [6] I. N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Canada Sect. III, 49 (1955), 19–22.
• [7] J. Luh, A note on commuting automorphisms of rings, Amer. Math. Monthly 77 (1970), 61–62.
• [8] J. H. Mayne, Centralizing automorphisms of prime rings, Canad. Mat. Bull. 19 (1976), 113–115.
• [9] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100.
• [10] J. Vukman, Identities with derivations and automorphisms on semiprime rings, Int. J. Math. Math. Sci. 7 (2005), 1031–1038.
• [11] B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609–614