Centralizers on semiprime rings

Joso Vukman

Commentationes Mathematicae Universitatis Carolinae (2001)

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

Abstract

top
The main result: Let R be a 2 -torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T ( x y x ) = x T ( y ) x holds for all x , y ∈ R . In this case T is a centralizer.

How to cite

top

Vukman, 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

top
  1. Brešar M., Vukman J., Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322. (1988) MR0943433
  2. Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. (1988) MR0929422
  3. Brešar M., Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. (1989) MR1029414
  4. Cusack J., Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324. (1975) Zbl0327.16020MR0399182
  5. Herstein I.N., Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. (1957) MR0095864
  6. Vukman J., An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae 40 (1999), 447-456. (1999) Zbl1014.16021MR1732490
  7. Zalar B., On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614. (1991) Zbl0746.16011MR1159807

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.