# On centralizers of semiprime rings

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 4, page 609-614
- ISSN: 0010-2628

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topZalar, Borut. "On centralizers of semiprime rings." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 609-614. <http://eudml.org/doc/247321>.

@article{Zalar1991,

abstract = {Let $\mathcal \{K\}$ be a semiprime ring and $T:\mathcal \{K\}\rightarrow \mathcal \{K\}$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \mathcal \{K\}$. Then $T$ is a left centralizer of $\mathcal \{K\}$. It is also proved that Jordan centralizers and centralizers of $\mathcal \{K\}$ coincide.},

author = {Zalar, Borut},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {semiprime ring; left centralizer; centralizer; Jordan centralizer; semi-prime free rings; additive maps; left centralizers; Jordan centralizers; right centralizers},

language = {eng},

number = {4},

pages = {609-614},

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

title = {On centralizers of semiprime rings},

url = {http://eudml.org/doc/247321},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Zalar, Borut

TI - On centralizers of semiprime rings

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

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

VL - 32

IS - 4

SP - 609

EP - 614

AB - Let $\mathcal {K}$ be a semiprime ring and $T:\mathcal {K}\rightarrow \mathcal {K}$ an additive mapping such that $T(x^2)=T(x)x$ holds for all $x\in \mathcal {K}$. Then $T$ is a left centralizer of $\mathcal {K}$. It is also proved that Jordan centralizers and centralizers of $\mathcal {K}$ coincide.

LA - eng

KW - semiprime ring; left centralizer; centralizer; Jordan centralizer; semi-prime free rings; additive maps; left centralizers; Jordan centralizers; right centralizers

UR - http://eudml.org/doc/247321

ER -

## References

top- Brešar M., Vukman J., On some additive mapping in rings with involution, Aequationes Math. 38 (1989), 178-185. (1989) MR1018911
- Brešar M., Zalar B., On the structure of Jordan $*$-derivations, Colloquium Math., to appear. MR1180629
- Herstein I.N., Topics in ring theory, University of Chicago Press, 1969. Zbl0232.16001MR0271135
- Herstein I.N., Theory of rings, University of Chicago Press, 1961.
- Johnson B.E., Sinclair A.M., Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073. (1968) Zbl0179.18103MR0239419
- Šemrl P., Quadratic functionals and Jordan $*$-derivations, Studia Math. 97 (1991), 157-165. (1991) MR1100685

## Citations in EuDML Documents

top- Joso Vukman, Centralizers on prime and semiprime rings
- Joso Vukman, An identity related to centralizers in semiprime rings
- Joso Vukman, Centralizers on semiprime rings
- Motoshi Hongan, Nadeem Ur Rehman, Radwan Mohammed AL-Omary, Lie ideals and Jordan triple derivations in rings
- Muhammad Anwar Chaudhry, Mohammad S. Samman, Free actions on semiprime rings
- S. Sara, M. Aslam, M.A. Javed, On centralizer of semiprime inverse semiring

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