An identity related to centralizers in semiprime rings

Joso Vukman

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 447-456
  • ISSN: 0010-2628

Abstract

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The purpose of this paper is to prove the following result: Let R be a 2 -torsion free semiprime ring and let T : R → R be an additive mapping, such that 2 T ( x 2 ) = T ( x ) x + x T ( x ) holds for all x ∈ R . In this case T is left and right centralizer.

How to cite

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Vukman, Joso. "An identity related to centralizers in semiprime rings." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 447-456. <http://eudml.org/doc/248388>.

@article{Vukman1999,
abstract = {The purpose of this paper is to prove the following result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping, such that $2T(x^2)=T(x)x+xT(x)$ holds for all $x\in R$. In this case $T$ is left and right centralizer.},
author = {Vukman, Joso},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {prime ring; semiprime ring; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer; prime rings; semiprime rings; Jordan derivations; right centralizers; left Jordan centralizers},
language = {eng},
number = {3},
pages = {447-456},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An identity related to centralizers in semiprime rings},
url = {http://eudml.org/doc/248388},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Vukman, Joso
TI - An identity related to centralizers in semiprime rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 447
EP - 456
AB - The purpose of this paper is to prove the following result: Let $R$ be a $2$-torsion free semiprime ring and let $T:R\rightarrow R$ be an additive mapping, such that $2T(x^2)=T(x)x+xT(x)$ holds for all $x\in R$. In this case $T$ is left and right centralizer.
LA - eng
KW - prime ring; semiprime ring; derivation; Jordan derivation; left (right) centralizer; left (right) Jordan centralizer; prime rings; semiprime rings; Jordan derivations; right centralizers; left Jordan centralizers
UR - http://eudml.org/doc/248388
ER -

References

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  1. Brešar M., Vukman J., Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-323. (1988) MR0943433
  2. Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) MR0929422
  3. Cusak J., Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) MR0399182
  4. Herstein I.N., Jordan derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) MR0095864
  5. Herstein I.N., Rings with involution, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, London, 1976. Zbl0495.16007MR0442017
  6. Posner E., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100. (1957) MR0095863
  7. Vukman J., Centralizers in prime and semiprime rings, Comment. Math. Univ. Carolinae 38 (1997), 231-240. (1997) MR1455489
  8. Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) Zbl0746.16011MR1159807

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