On Approximate n-Jordan Homomorphisms

• Autorzy: Eszter Gselmann
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper it to characterize n-Jordan homomorphisms and to investigate their connection with n-homomorphisms as well as homomorphisms. Furthermore, the following implication is also verified: if a function $\varphi$ is additive and (for a fixed integer $n\geq 2$) the mapping $x\mapsto\varphi (x^n) - \varphi (x)^n$ satisfies some mild regularity assumption, then the function $\varphi$ is an n-homomorphism or it is a continuous additive function. (original abstract)

Słowa kluczowe

EN

Mathematics; Algebra

PL

Matematyka; Algebra

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2014
• Tom: 28
• Strony: 47--58

Twórcy

autor

Eszter Gselmann

• University of Debrecen, Hungary

Bibliografia

• Ancochea G., Le théorème de von Staudt en géométrie projective quaternionienne, J. Reine Angew. Math. 184 (1942), 193-198.
• Badora R., On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), no. 2, 589-597.
• Brešar M., Martindale 3rd W.S., Miers C.R., Maps preserving nth powers, Comm. Algebra 26 (1998), no. 1, 117-138.
• Eshaghi Gordji M., n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 (2009), no. 1, 159-164.
• Hejazian Sh., Mirzavaziri M., Moslehian M.S., n-homomorphisms, Bull. Iranian Math. Soc. 31 (2005), no. 1, 13-23.
• Herstein I.N., Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331-341.
• Jacobson N., Rickart C.E., Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479-502.
• Kaplansky I., Semi-automorphisms of rings, Duke Math. J. 14 (1947), 521-525.
• Kuczma M., An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality, Second edition, Birkhäuser Verlag, Basel, 2009.
• Šemrl M., Nonlinear perturbations of homomorphisms on C(X), Quart. J. Math. Oxford Ser. (2) 50 (1999), no. 197, 87-109.
• Šemrl P., Almost multiplicative functions and almost linear multiplicative functionals, Aequationes Math. 63 (2002), no. 1-2, 180-192.
• Székelyhidi L., Regularity properties of polynomials on groups, Acta Math. Hungar. 45 (1985), no. 1-2, 15-19.
• Zelazko W., A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85.