On left $(\theta,\varphi)$-derivations of prime rings
Ashraf, Mohammad
Archivum Mathematicum, Tome 041 (2005), p. 157-166 / Harvested from Czech Digital Mathematics Library
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Let $R$ be a $2$-torsion free prime ring. Suppose that $\theta , \phi $ are automorphisms of $R$. In the present paper it is established that if $R$ admits a nonzero Jordan left $(\theta ,\theta )$-derivation, then $R$ is commutative. Further, as an application of this resul it is shown that every Jordan left $(\theta ,\theta )$-derivation on $R$ is a left $(\theta ,\theta )$-derivation on $R$. Finally, in case of an arbitrary prime ring it is proved that if $R$ admits a left $(\theta ,\phi )$-derivation which acts also as a homomorphism (resp. anti-homomorphism) on a nonzero ideal of $R$, then $d=0$ on $R$.

Publié le : 2005-01-01
Classification:  16N60,  16W25 
@article{107946,
     author = {Mohammad Ashraf},
     title = {On left $(\theta,\varphi)$-derivations of prime rings},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {157-166},
     zbl = {1114.16031},
     mrnumber = {2164665},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107946}
}

Ashraf, Mohammad. On left $(\theta,\varphi)$-derivations of prime rings. Archivum Mathematicum, Tome 041 (2005) pp. 157-166. http://gdmltest.u-ga.fr/item/107946/

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