Centralizers on semiprime rings
Vukman, Joso
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 237-245 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2001-01-01
Classification:  16A12,  16A68,  16A72,  16N60,  16W10,  16W20 
@article{119239,
     author = {Joso Vukman},
     title = {Centralizers on semiprime rings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {237-245},
     zbl = {1057.16029},
     mrnumber = {1832143},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119239}
}

Vukman, Joso. Centralizers on semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 237-245. http://gdmltest.u-ga.fr/item/119239/

Brešar M.; Vukman J. Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322. (1988) | MR 0943433

Brešar M. Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) | MR 0929422

Brešar M. Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. (1989) | MR 1029414

Cusack J. Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) | MR 0399182 | Zbl 0327.16020

Herstein I.N. Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) | MR 0095864

Vukman J. An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae 40 (1999), 447-456. (1999) | MR 1732490 | Zbl 1014.16021

Zalar B. On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) | MR 1159807 | Zbl 0746.16011