Existentially generated subfields of large fields

2017/10/09 by Anscombe, Sylvy · 1 citation
#03C60 #11U09 #12J10 #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1710.03353

Abstract

We study subfields of large fields which are generated by infinite existentially definable subsets. We say that such subfields are existentially generated. Let L be a large field of characteristic exponent p, and let E⊆ L be an infinite existentially generated subfield. We show that E contains L^(pⁿ), the pⁿ-th powers in L, for some n

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