When an Extension of Nagata Rings Has Only Finitely Many Intermediate Rings, Each of Those Is a Nagata Ring

David E. Dobbs, Gabriel Picavet and Martine Picavet-L’Hermitte

International Journal of Mathematics and Mathematical Sciences, 2014, vol. 2014, 1-13

Abstract:

Let be an extension of commutative rings, with X an indeterminate, such that the extension of Nagata rings has FIP (i.e., has only finitely many -subalgebras). Then, the number of -subalgebras of equals the number of R -subalgebras of S . In fact, the function from the set of R -subalgebras of S to the set of -subalgebras of given by is an order-isomorphism.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:315919

DOI: 10.1155/2014/315919

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