(3) Suppose that S is a commutative ring with identity, and R is a subring (that also contains 16S). We assume that S is
Posted: Thu May 12, 2022 7:40 am
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(3) Suppose that S is a commutative ring with identity, and R is a subring (that also contains 16S). We assume that S is finitely generated over R, i.e., there exist a1, A2, ..., An ES such that every element of S is of the form p(a1, A2, ..., An) for some polynomial p(x1, C2, ..., Xn) with coefficients in R. Show that if R is noetherian, then S is noetherian.