Abstract

We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if A C B are domains such that A is an LFD universally going-down domain and B is algebraic over A, then the inclusion map A[X 1 , ..., X n ] → B[X 1 ,..., X n ] satisfies GB for each n ≥ 0. However, for any nonzero ring A and indeterminate X over A, the inclusion map A → A[X] is not universally (S)GB.

Highlights

  • BLAISE PASCALVolume 10, no 2 (2003), p. 245-260. (http://ambp.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://ambp.cedram.org/legal/)

  • All rings considered below are commutative with identity; all ring extensions and ring homomorphisms are unital

  • A.) Following [18], we say that a ring homomorphism f : A → B satisfies

Read more

Summary

BLAISE PASCAL

Volume 10, no 2 (2003), p. 245-260. (http://ambp.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://ambp.cedram.org/legal/). (http://ambp.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://ambp.cedram.org/legal/). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Publication éditée par le laboratoire de mathématiques de l’université Blaise-Pascal, UMR 6620 du CNRS. Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/

Introduction
Logical independence and transfer results

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.