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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The local rings of global dimension two
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by Wolmer V. Vasconcelos
Proc. Amer. Math. Soc. 35 (1972), 381-386
DOI: https://doi.org/10.1090/S0002-9939-1972-0308115-6

Abstract:

A commutative local ring A of global dimension two conforms to the following description: (a) If the maximal ideal M is either principal or not finitely generated then A is a valuation domain. (b) Otherwise M is generated by a regular sequence of two elements but the ring is not necessarily noetherian. It will be noetherian if and only if it is completely integrally closed.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 381-386
  • MSC: Primary 13H99
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0308115-6
  • MathSciNet review: 0308115