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A simple algorithm for cyclic vectors. (English) Zbl 0621.13003
Let R be a commutative ring, $$\delta$$ : $$R\to R$$ a derivation of R, V a free R-module of rank $$n\geq 1$$, and $$D: V\to V$$ an additive map with $$D(fv)=\delta (f)v+fD(v)$$ for all $$f\in R$$, $$v\in V$$. In several cases the author gives an explicit construction of a cyclic vector v of (V,D), i.e. a vector $$v\in V$$ such that v, $$Dv,...,D^{n-1}v$$ is a basis of V.
Reviewer: H.Wiebe

##### MSC:
 13B10 Morphisms of commutative rings 13C10 Projective and free modules and ideals in commutative rings
##### Keywords:
free module; derivation; cyclic vector
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