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(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then...

(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then the equation ax+b=c has a unique solution.

(b) If R is a commutative ring and x1,x2,...,xn are independent variables over R, prove that R[x σ(1),x σ (2),...,x σ (n)] is isomorphic to R[x1,x2,...,xn] for any permutation σ of the set {1,2,...,n}

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