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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)
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