Derivations as homomorphisms or anti-homomorphisms in differentially semiprime rings

M. P. Lukashenko
Faculty of Mathematics and Informatics, Preñarpathian National University of Vasyl Stefanyk
Let $R$ be a ring with an identity, $U$ a nonzero right $d$-ideal and $d \in\mathop{\rm Der} R$. We prove that if $R$ is $d$-semiprime and $d$ is a homomorphism (respectively an anti-endomorphism) of $R$ (respectively acts as a homomorphism on $U$), then $d=0$. If $R$ is $d$-prime and $d$ acts as an anti-homomorphism on $U$, then $d=0$.
$d$-ideal; homomorphism; differentially semiprime ring
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