Automorphism groups of fields |
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Authors: | Manfred Dugas Rüdiger Göbel |
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Institution: | 1. Department of Mathematics, Baylor University, 76798, Waco, Texas, U.S.A. 2. Fachbereich 6, Mathematik und Informatik, Universit?t Essen, GHS, Universit?tsstr. 3, 45117, Essen, Germany
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Abstract: | We consider pairs (K,G) of an infinite field K or a formally real field K and a group G and want to find extension fields
F of K with automorphism group G. If K is formally real then we also want F to be formally real and G must be right orderable.
Besides showing the existence of the desired extension fields F, we are mainly interested in the question about the smallest
possible size of such fields. From some combinatorial tools, like Shelah’s Black Box, we inherit jumps in cardinalities of
K and F respectively. For this reason we apply different methods in constructing fields F: We use a recent theorem on realizations
of group rings as endomorphism rings in the category of free modules with distinguished submodules. Fortunately this theorem
remains valid without cardinal jumps. In our main result (Theorem 1) we will show that for a large class of fields the desired
result holds for extension fields of equal cardinality.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag |
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