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Hilbert Rings Arising as Pullbacks

Published online by Cambridge University Press:  20 November 2018

David F. Anderson ,
David E. Dobbs  and
Marco Fontana
David F. Anderson
Affiliation:
University of Tennessee Knoxville, Tennessee 37996-1300 U.S.A.
David E. Dobbs
Affiliation:
University of Tennessee Knoxville, Tennessee 37996-1300 U.S.A.
Marco Fontana
Affiliation:
Università di Roma 00185, Roma Italy
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Abstract

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Let 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.

Keywords

13A1513D9913G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 431 - 438
Copyright
Copyright © Canadian Mathematical Society 1992

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