# Article

Full entry | PDF   (0.1 MB)
Keywords:
prime ring; semiprime ring; derivation; Jordan derivation; Jordan triple derivation; left (right) centralizer; left (right) Jordan centralizer; centralizer
Summary:
The main result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping. Suppose that $T(xyx) = xT(y)x$ holds for all $x,y\in R$. In this case $T$ is a centralizer.
References:
[1] Brešar M., Vukman J.: Jordan derivations on prime rings. Bull. Austral. Math. Soc. 37 (1988), 321-322. MR 0943433
[2] Brešar M.: Jordan derivations on semiprime rings. Proc. Amer. Math. Soc. 104 (1988), 1003-1006. MR 0929422
[3] Brešar M.: Jordan mappings of semiprime rings. J. Algebra 127 (1989), 218-228. MR 1029414
[4] Cusack J.: Jordan derivations on rings. Proc. Amer. Math. Soc. 53 (1975), 321-324. MR 0399182 | Zbl 0327.16020
[5] Herstein I.N.: Jordan derivations of prime rings. Proc. Amer. Math. Soc. 8 (1957), 1104-1110. MR 0095864
[6] Vukman J.: An identity related to centralizers in semiprime rings. Comment. Math. Univ. Carolinae 40 (1999), 447-456. MR 1732490 | Zbl 1014.16021
[7] Zalar B.: On centralizers of semiprime rings. Comment. Math. Univ. Carolinae 32 (1991), 609-614. MR 1159807 | Zbl 0746.16011

Partner of