Abstract
LetR be a Krull subring of a ring of polynomialsk[x 1, …, xn] over a fieldk. We prove that ifR is generated by monomials overk thenr is affine. We also construct an example of a non-affine Krull ringR, such thatk[x, xy]⊂R⊂k[x, y], and a non-Noetherian Krull ringS, such thatk[x, xy, z]⊂S⊂k[x, y, z].
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Wajnryb, B. Finiteness conditions in Krull subrings of a ring of polynomials. Israel J. Math. 43, 169–176 (1982). https://doi.org/10.1007/BF02761729
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DOI: https://doi.org/10.1007/BF02761729