Free actions on semiprime rings
Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 197-208.

Voir la notice de l'article dans Czech Digital Mathematics Library

We identify some situations where mappings related to left centralizers, derivations and generalized $(\alpha ,\beta )$-derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation $T$, of a semiprime ring $R$ the mapping $\psi \: R \rightarrow R$ defined by $\psi (x)=T(x) x - x T(x)$ for all $x \in R$ is a free action. We also show that for a generalized $(\alpha , \beta )$-derivation $F$ of a semiprime ring $R,$ with associated $(\alpha , \beta )$-derivation $d,$ a dependent element $a$ of $F$ is also a dependent element of $\alpha + d.$ Furthermore, we prove that for a centralizer $f$ and a derivation $d$ of a semiprime ring $R$, $\psi = d\circ f$ is a free action.
DOI : 10.21136/MB.2008.134055
Classification : 16N60, 16W20, 16W25
Mots-clés : prime ring; semiprime ring; dependent element; free action; centralizer; derivation 
@article{10_21136_MB_2008_134055,
     author = {Chaudhry, Muhammad Anwar and Samman, Mohammad S.},
     title = {Free actions on semiprime rings},
     journal = {Mathematica Bohemica},
     pages = {197--208},
     publisher = {mathdoc},
     volume = {133},
     number = {2},
     year = {2008},
     doi = {10.21136/MB.2008.134055},
     mrnumber = {2428315},
     zbl = {1170.16026},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.134055/}
}
TY  - JOUR
AU  - Chaudhry, Muhammad Anwar
AU  - Samman, Mohammad S.
TI  - Free actions on semiprime rings
JO  - Mathematica Bohemica
PY  - 2008
SP  - 197
EP  - 208
VL  - 133
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.134055/
DO  - 10.21136/MB.2008.134055
LA  - en
ID  - 10_21136_MB_2008_134055
ER  - 
%0 Journal Article
%A Chaudhry, Muhammad Anwar
%A Samman, Mohammad S.
%T Free actions on semiprime rings
%J Mathematica Bohemica
%D 2008
%P 197-208
%V 133
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.134055/
%R 10.21136/MB.2008.134055
%G en
%F 10_21136_MB_2008_134055
Chaudhry, Muhammad Anwar; Samman, Mohammad S. Free actions on semiprime rings. Mathematica Bohemica, Tome 133 (2008) no. 2, pp. 197-208. doi : 10.21136/MB.2008.134055. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.134055/

Cité par Sources :