Question: 3. Let k be a field, and consider the polynomial ring k[x, y] in two variables x, y over k. Let R : = kx,

3. Let k be a field, and consider the polynomial ring k[x, y] in two variables x, y over k. Let R : = kx, xy, ..., any"-1 , ... ] be the subring of k(x, y] generated by R and the monomials xy"- (for n = 1, 2, ...). (a) Show that R and kx, y] have the same fields of fractions. (b) Show that R is not noetherian

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