Geodesic
Hilbert Rings Arising as Pullbacks
Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 431-438

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DOI

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.
DOI : 10.4153/CMB-1992-057-4
Mots-clés : 13A15, 13D99, 13G05 
Anderson, David F.; Dobbs, David E.; Fontana, Marco. Hilbert Rings Arising as Pullbacks. Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 431-438. doi: 10.4153/CMB-1992-057-4
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     author = {Anderson, David F. and Dobbs, David E. and Fontana, Marco},
     title = {Hilbert {Rings} {Arising} as {Pullbacks}},
     journal = {Canadian mathematical bulletin},
     pages = {431--438},
     year = {1992},
     volume = {35},
     number = {4},
     doi = {10.4153/CMB-1992-057-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-057-4/}
}
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