On a Functional Equation Related to Two-Sided Centralizers

Kosi-Ulbl, Irena

doi:10.1515/amsil-2017-0014

Abstract

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)x^n-1+ xT(x^n-2)x + x^n-1T(x), x ∈R, is also fulfilled. Then T is a two-sided centralizer.

References

[1] Beidar K.I., Brešar M., Chebotar M.A., Martindale W.S., 3rd, On Herstein’s Lie map conjectures. II, J. Algebra 238 (2001), 239-264.10.1006/jabr.2000.8628
Search in Google Scholar Back to article
[2] 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.
Search in Google Scholar Back to article
[3] Benkovic D., Eremita D., Vukman J., A characterization of the centroid of a prime ring, Studia Sci. Math. Hungar. 45 (2008), 379-394.
Search in Google Scholar Back to article
[4] Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.10.1090/S0002-9939-1988-0929422-1
Open DOI Search in Google Scholar Back to article
[5] Brešar M., Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.10.1016/0021-8693(89)90285-8
Search in Google Scholar Back to article
[6] Brešar M., Vukman J., Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322.10.1017/S0004972700026927
Search in Google Scholar Back to article
[7] Brešar M., Vukman J., Jordan (ᶿ;ᶲ)-derivations, Glas. Mat. Ser. III 26(46) (1991), 13-17.
Search in Google Scholar Back to article
[8] Cusack J.M., Jordan derivations on rigs, Proc. Amer. Math. Soc. 53 (1975), 321-324.10.1090/S0002-9939-1975-0399182-5
Search in Google Scholar Back to article
[9] Herstein I.N., Jordan derivations of prime rings, Proc. Amer. Mah. Soc. 8 (1957), 1104-1110.10.1090/S0002-9939-1957-0095864-2
Search in Google Scholar Back to article
[10] Molnár L., On centralizers of an H_-algebra, Publ. Math. Debrecen 46 (1995), 89-95.10.5486/PMD.1995.1495
Search in Google Scholar Back to article
[11] Vukman J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin. 40 (1999), 447-456.
Search in Google Scholar Back to article
[12] Vukman J., Centralizers on semiprime rings, Comment. Math. Univ. Carolin. 42 (2001), 237-245.
Search in Google Scholar Back to article
[13] Vukman J., Identities related to derivations and centralizers on standard operator algebras, Taiwanese J. Math. 11 (2007), 255-265.
Search in Google Scholar Back to article
[14] Vukman J., Kosi-Ulbl I., An equation related to centralizers in semiprime rings, Glas. Mat. Ser. III 38(58) (2003), 253-261.10.3336/gm.38.2.04
Search in Google Scholar Back to article
[15] Vukman J., Kosi-Ulbl I., Centralisers on rings and algebras, Bull. Austral. Math. Soc. 71 (2005), 225-234.10.1017/S000497270003820X
Search in Google Scholar Back to article
[16] Vukman J., Kosi-Ulbl I., A remark on a paper of L. Molnár, Publ. Math. Debrecen 67 (2005), 419-421.10.5486/PMD.2005.3221
Search in Google Scholar Back to article
[17] Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609-614.
Search in Google Scholar Back to article

On a Functional Equation Related to Two-Sided Centralizers

Abstract

Paradigm

My account