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The catenarian property of the polynomial rings over a Prüfer domain

Part of the Lecture Notes in Mathematics book series (LNM,volume 1146)

Abstract

This paper gives complete proofs of the following result: let R be a locally finite dimensional Prüfer domain; then, the polynomial ring R[T1,..,Tr] is catenarian for every r⩾1. The main techniques used in the proof are pull-backs and a function introduced here to measure the extent to which prime ideals in polynomial domains fail to be extended.

Work performed under the auspices of G.N.S.A.G.A. (Consiglio Nazionale delle Ricerche).

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© 1985 Springer-Verlag

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Bouvier, A., Fontana, M. (1985). The catenarian property of the polynomial rings over a Prüfer domain. In: Malliavin, MP. (eds) Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074546

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  • DOI: https://doi.org/10.1007/BFb0074546

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  • Print ISBN: 978-3-540-15686-4

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