# Centralizers on semiprime rings

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 2, page 237-245
- ISSN: 0010-2628

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topVukman, Joso. "Centralizers on semiprime rings." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 237-245. <http://eudml.org/doc/248764>.

@article{Vukman2001,

abstract = {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.},

author = {Vukman, Joso},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {prime ring; semiprime ring; derivation; Jordan derivation; Jordan triple derivation; left (right) centralizer; left (right) Jordan centralizer; centralizer; prime rings; semiprime rings; Jordan derivations; Jordan triple derivations; Jordan centralizers; left centralizers; additive mappings},

language = {eng},

number = {2},

pages = {237-245},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Centralizers on semiprime rings},

url = {http://eudml.org/doc/248764},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Vukman, Joso

TI - Centralizers on semiprime rings

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 2

SP - 237

EP - 245

AB - 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.

LA - eng

KW - prime ring; semiprime ring; derivation; Jordan derivation; Jordan triple derivation; left (right) centralizer; left (right) Jordan centralizer; centralizer; prime rings; semiprime rings; Jordan derivations; Jordan triple derivations; Jordan centralizers; left centralizers; additive mappings

UR - http://eudml.org/doc/248764

ER -

## References

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- Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) MR0929422
- Brešar M., Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. (1989) MR1029414
- Cusack J., Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) Zbl0327.16020MR0399182
- Herstein I.N., Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) MR0095864
- Vukman J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae 40 (1999), 447-456. (1999) Zbl1014.16021MR1732490
- Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) Zbl0746.16011MR1159807

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