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arXiv · 1111.1205

Computable Categoricity for Algebraic Fields with Splitting Algorithms

Russell Miller·Alexandra Shlapentokh
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Abstract

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of elements of $F$ belong to the same orbit under automorphisms. We also show that this criterion is equivalent to the relative computable categoricity of $F$.

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BibTeXRIS

Russell Miller, Alexandra Shlapentokh. 2011-11-04. Computable Categoricity for Algebraic Fields with Splitting Algorithms. https://arxiv.org/abs/1111.1205

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