Glasnik Matematicki, Vol. 46, No. 2 (2011), 339-349.
IDENTITIES WITH DERIVATIONS IN RINGS
Ajda Fošner, Maja Fošner and Joso Vukman
Faculty of Management, University of Primorska, Cankarjeva 5, 6104 Koper, Slovenia
e-mail: ajda.fosner@fm-kp.si
Faculty of Logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
e-mail: maja.fosner@uni-mb.si
Department of Mathematics and Computer Science,
Faculty of Natural Sciences and Mathematics,
University of Maribor,
Koroška cesta 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si
Abstract. In this paper we investigate identities with derivations
in rings. We prove, for example the following result. Let m ≥ 1,n ≥ 1 be some fixed integers and let
R be a 6nm2(2m+n-3)!-torsion free semiprime ring. Suppose there exists a derivation
D:R → R satisfying the relation
[[D(xm),xn] ,D(xm)]=0 for all x R.
In this case D maps R into its center.
2000 Mathematics Subject Classification.
16N60.
Key words and phrases. Prime ring, semiprime ring, derivation.
Full text (PDF) (free access)
DOI: 10.3336/gm.46.2.06
References:
- K. I. Beidar, W. S. Martindale III and A. V. Mikhalev,
Rings with generalized identities,
Marcel Dekker Inc., New York, 1996.
MathSciNet
- M. Brešar, Jordan derivations on semiprime rings,
Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
MathSciNet
CrossRef
- C. L. Chuang,
On compositions of derivations of prime rings,
Proc. Amer. Math. Soc. 108 (1990), 647-652.
MathSciNet
CrossRef
- Q. Deng and H. E. Bell,
On derivations and commutativity in semiprime rings,
Commun. Algebra 23 (1995), 3705-3713.
MathSciNet
CrossRef
- A. Fošner, M. Fošner and J. Vukman, An identity
with derivations on rings and Banach algebras, Demonstratio Math. XLI
(2008), 525-530.
MathSciNet
- T. K. Lee,
Semiprime rings with differential identities,
Bull. Inst. Math. Acad. Sinica 20 (1992), 27-38.
MathSciNet
- E. C. Posner,
Derivations in prime rings,
Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
MathSciNet
CrossRef
- J. Vukman, Derivations on semiprime rings,
Bull. Austral. Math. Soc. 53 (1996), 353-359.
MathSciNet
CrossRef
- J. Vukman,
Identities with derivations on rings and Banach algebras,
Glas. Mat. Ser. III 40(60) (2005), 189-199.
MathSciNet
CrossRef
Glasnik Matematicki Home Page