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RINGS WITH TRIVIAL FML-INVARIANT

  • DANIEL DAIGLEEmail author
Article

Abstract

Let k be a field of characteristic zero and B a commutative integral domain that is also a finitely generated k-algebra. It is well known that if k is algebraically closed and the “field Makar-Limanov” invariant FML(B) is equal to k, then B is unirational over k. This article shows that, when k is not assumed to be algebraically closed, the condition FML(B) = k implies that there exists a nonempty Zariski-open subset U of Spec B with the following property: for each prime ideal \( \mathfrak{p} \)U, the κ(\( \mathfrak{p} \))-algebra κ(\( \mathfrak{p} \))⊗kB can be embedded in a polynomial ring in n variables over κ(\( \mathfrak{p} \)), where n = dim B and κ(\( \mathfrak{p} \)) = \( {B}_{\mathfrak{p}}/\mathfrak{p}{B}_{\mathfrak{p}} \).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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