On centralizers of semiprime rings

Borut Zalar

Commentationes Mathematicae Universitatis Carolinae (1991)

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

Abstract

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Let 𝒦 be a semiprime ring and T : 𝒦 → 𝒦 an additive mapping such that T ( x 2 ) = T ( x ) x holds for all x ∈ 𝒦 . Then T is a left centralizer of 𝒦 . It is also proved that Jordan centralizers and centralizers of 𝒦 coincide.

How to cite

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Zalar, 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

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

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