Let R be a ring, and let n E N be a natural number. Consider the...

 

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Let R be a ring, and let n E N be a natural number. Consider the polynomial ring R[,...,n] in n variables ,. n over . Show that for any permutation Sn = Perm({1,...,n}) of the set {1,...,n}, there is a unique ring automorphism f of R[x,...,xn] which fixes all elements of R and which sends x to (i) for each i 1,..., n. Let R be a ring, and let n E N be a natural number. Consider the polynomial ring R[,...,n] in n variables ,. n over . Show that for any permutation Sn = Perm({1,...,n}) of the set {1,...,n}, there is a unique ring automorphism f of R[x,...,xn] which fixes all elements of R and which sends x to (i) for each i 1,..., n.