Abstract
Let K⊂M be a finite field extension. An intermediate field L is called “invariant” if there is an affine algebraic K-group acting on M with L as its invariant field. The question, which intermediate fields are invariant, was studied by Begueri [1] for purely inseparable extensions and by Sweedler [6] for arbitrary extensions, but only for a restricted class of groups. In this paper Begueri's result is generalized to arbitrary field extensions. Additionally it is shown that one can check whether a given intermediate field is invariant or not by computing the rank of certain matrices. As an application we get a class of invariant intermediate fields.
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