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

Artemovych, O. D.

Algebra Discrete Math. 2004, No. 2, 17-22 (2004).

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)

Keywords:

semi-Artinian rings; differentially trivial rings; rigid rings