If Sn, then the map K(x 1 , 'X n ) K(x 1 , 'X n ) given by is a K automorphism of K(x 1 , , x n ) f(x, ,xn), f(xo(1), Xo(n)) g(x, ,xn) g(xo(1), , Xo(n)) ,...

Yes the given map is a Kautomorphism of Kx1 xn where K is a field and Sn is the symmetric group on n ...

If Sn, then the map K(x 1 , ... 'X n ) - K(x 1

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If σ ϵ Sn, then the map K(x₁, ... 'X_n) - K(x₁, ... 'X_n) given by

is a K-automorphism of K(x₁, •.. , x_n).

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 16, 2023 03:50 AM

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If Sn, then the map K(x 1 , ... 'X n ) - K(x 1

Question:

f(x₁,...,xn), f(xo(1), Xo(n)) g(x₁,...,xn) g(xo(1),..., Xo(n)) ...,

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Yes the given map is a Kautomorphism of Kx1 xn where K is a field and Sn is the symmetric group on n ...View the full answer

Algebra Graduate Texts In Mathematics 73

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