Abstract
AbstractLet R be the pullback A ×cB, where B → C is a surjective homomorphism of commutative rings and A is a subring of C. It is shown that R and C are Hilbert rings if and only if A and B are Hilbert rings. Applications are given to the D + XE[X], D + M, and D + (X1,..., Xn)Ds[X1,..., Xn] constructions. For these constructions, new examples are given of Hilbert domains R which are unruly, in the sense that R is non-Noetherian and each of its maximal ideals is finitely generated. Related examples are also given.
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