# On left $(\theta ,\varphi )$-derivations of prime rings

Archivum Mathematicum (2005)

- Volume: 041, Issue: 2, page 157-166
- ISSN: 0044-8753

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topAshraf, Mohammad. "On left $(\theta ,\varphi )$-derivations of prime rings." Archivum Mathematicum 041.2 (2005): 157-166. <http://eudml.org/doc/249503>.

@article{Ashraf2005,

abstract = {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 $R$.},

author = {Ashraf, Mohammad},

journal = {Archivum Mathematicum},

keywords = {Lie ideals; prime rings; derivations; Jordan left derivations; left derivations; torsion free rings; Lie ideals; Jordan left derivations},

language = {eng},

number = {2},

pages = {157-166},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On left $(\theta ,\varphi )$-derivations of prime rings},

url = {http://eudml.org/doc/249503},

volume = {041},

year = {2005},

}

TY - JOUR

AU - Ashraf, Mohammad

TI - On left $(\theta ,\varphi )$-derivations of prime rings

JO - Archivum Mathematicum

PY - 2005

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 041

IS - 2

SP - 157

EP - 166

AB - 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 $R$.

LA - eng

KW - Lie ideals; prime rings; derivations; Jordan left derivations; left derivations; torsion free rings; Lie ideals; Jordan left derivations

UR - http://eudml.org/doc/249503

ER -

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