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A Duality for Skew Field Extensions



A duality is set up for skew field extensions. Dual extensions are constructed using lambda-closed fields. Inner, outer, central and plain extensions are introduced, and some of their properties are derived. An arbitrary extension is decomposed into four extensions of basic type. Galois theory is built up using duality and some theory of diagonal extensions: the dual extensions of Galois extensions. Implications are given for prime extensions and for extensions of a field which is of finite dimension over its center.
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