## Differentially trivial and rigid right semi-Artinian rings.(English)Zbl 1067.16059

Summary: We obtain a characterization of right semi-Artinian rings which have only trivial derivations and prove that a rigid (i.e. has only the trivial ring endomorphisms) right semi-Artinian ring $$R$$ is a field or isomorphic to some $$\mathbb{Z}_{p^n}$$.

### MSC:

 16W25 Derivations, actions of Lie algebras 16W20 Automorphisms and endomorphisms 16P20 Artinian rings and modules (associative rings and algebras)