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Let F be a field and let R=F[x] be the polynomial ring in one variable over F. Consider the ring S=R[x 2 , x 3
Let F be a field and let R=F[x] be the polynomial ring in one variable over F. Consider the ring S=R[x2, x3, . . .] obtained by adjoining xii Z2 to R, where the xi satisfy =x, =x2, =x3, . . . .Prove that in the ring there is no factorization into irreducible factors.
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