Development and Applications of Galois Theory

Part of the Universitext book series (UTX)


We now apply our general theory to the case of symmetric functions. We let D be an arbitrary field and set E=D(X1,⋯, Xd), the field of rational functions in the variables X1,⋯, Xd. Then the symmetric group Sd acts on E by permuting X1,⋯,Xd


Galois Group Galois Theory Galois Extension Primitive Element Irreducible Polynomial 
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© Springer Science+Business Media, Inc. 2006

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