On a Functional Equation Related to Two-Sided Centralizers

• Autorzy: Irena Kosi-Ulbl
• Języki publikacji: EN

Abstrakty

EN

The main aim of this manuscript is to prove the following result. Let n > 2 be a fixed integer and R be a k-torsion free semiprime ring with identity, where k ∈ {2, n - 1, n}. Let us assume that for the additive mapping T : R→ R 3T(xn) = T(x)xn-1+ xT(xn-2)x + xn-1T(x), x ∈R, is also fulfilled. Then T is a two-sided centralizer. (original abstract)

Słowa kluczowe

EN

Mathematics; Algebra; Functional equation

PL

Matematyka; Algebra; Równanie funkcyjne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2018
• Tom: 32
• Strony: 227--235

Twórcy

autor

Irena Kosi-Ulbl

• University of Maribor, Slovenia

Bibliografia

• Beidar K.I., Brešar M., Chebotar M.A., Martindale W.S., 3rd, On Herstein's Lie map conjectures. II, J. Algebra 238 (2001), 239-264.
• Beidar K.I., Martindale W.S., III, Mikhalev A.V., Rings with generalized identities, Monographs and Textbooks in Pure and Applied Mathematics 196, Marcel Dekker Inc., New York, 1996.
• Benkovič D., Eremita D., Vukman J., A characterization of the centroid of a prime ring, Studia Sci. Math. Hungar. 45 (2008), 379-394.
• Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
• Brešar M., Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.
• Brešar M., Vukman J., Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322.
• Brešar M., Vukman J., Jordan (θ,ϕ)-derivations, Glas. Mat. Ser. III 26(46) (1991), 13-17.
• Cusack J.M., Jordan derivations on rigs, Proc. Amer. Math. Soc. 53 (1975), 321-324.
• Herstein I.N., Jordan derivations of prime rings, Proc. Amer. Mah. Soc. 8 (1957), 1104-1110.
• Molnár L., On centralizers of an H*-algebra, Publ. Math. Debrecen 46 (1995), 89-95.
• Vukman J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin. 40 (1999), 447-456.
• Vukman J., Centralizers on semiprime rings, Comment. Math. Univ. Carolin. 42 (2001), 237-245.
• Vukman J., Identities related to derivations and centralizers on standard operator algebras, Taiwanese J. Math. 11 (2007), 255-265.
• Vukman J., Kosi-Ulbl I., An equation related to centralizers in semiprime rings, Glas. Mat. Ser. III 38(58) (2003), 253-261.
• Vukman J., Kosi-Ulbl I., Centralisers on rings and algebras, Bull. Austral. Math. Soc. 71 (2005), 225-234.
• Vukman J., Kosi-Ulbl I., A remark on a paper of L. Molnár, Publ. Math. Debrecen 67 (2005), 419-421.
• Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609-614.

Identyfikatory

DOI

10.1515/amsil-2017-0014