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Intersections of two cofinite subfields

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Abstract.

Let F be a field finite-dimensional over subfields A and B. It is known from Galois theory that the degree \( [F : A \cap B] \) can be infinite. If F is purely inseparable over B and finitely generated over the prime field, this cannot happen; but it can happen when F is not finitely generated.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    W. C. Waterhouse

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  1. W. C. Waterhouse
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Correspondence to W. C. Waterhouse.

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Received: 15 July 2003

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Waterhouse, W.C. Intersections of two cofinite subfields. Arch. Math. 82, 298–300 (2004). https://doi.org/10.1007/s00013-003-4872-0

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  • DOI: https://doi.org/10.1007/s00013-003-4872-0

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