Distinguished subfields

Deveney, James K.; Mordeson, John N.

doi:10.1090/S0002-9947-1980-0570785-4

Distinguished subfields
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by James K. Deveney and John N. Mordeson

Trans. Amer. Math. Soc. 260 (1980), 185-193

DOI: https://doi.org/10.1090/S0002-9947-1980-0570785-4

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Abstract:

Let L be a finitely generated nonalgebraic extension of a field K of characteristic $p \ne 0$. A maximal separable extension D of K in L is distinguished if $L \subseteq {K^{{p^{ - n}}}}(D)$ for some n. Let d be the transcendence degree of L over K. If every maximal separable extension of K in L is distinguished, then every set of d relatively p-independent elements is a separating transcendence basis for a distinguished subfield. Conversely, if $K({L^p})$ is separable over K, this condition is also sufficient. A number of properties of such fields are determined and examples are presented illustrating the results.

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