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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Essential domains and two conjectures in dimension theory
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by M. Fontana and S. Kabbaj PDF
Proc. Amer. Math. Soc. 132 (2004), 2529-2535 Request permission

Abstract:

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.
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Additional Information
  • M. Fontana
  • Affiliation: Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo San L. Murialdo 1, 00146 Roma, Italy
  • Email: fontana@mat.uniroma3.it
  • S. Kabbaj
  • Affiliation: Department of Mathematics, P.O. Box 5046, KFUPM, Dhahran 31261, Saudi Arabia
  • Email: kabbaj@kfupm.edu.sa
  • Received by editor(s): January 15, 2003
  • Published electronically: April 21, 2004
  • Additional Notes: The first author was partially supported by a research grant MIUR 2001/2002 (Cofin 2000-MM01192794). The second author was supported by the Arab Fund for Economic and Social Development
    This work was done while both authors were visiting Harvard University
  • Communicated by: Bernd Ulrich
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 2529-2535
  • MSC (2000): Primary 13C15, 13F20, 13F05, 13G05, 13B02, 13B30
  • DOI: https://doi.org/10.1090/S0002-9939-04-07502-1
  • MathSciNet review: 2054776