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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Reductions of ideals in Prüfer domains
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by James H. Hays PDF
Proc. Amer. Math. Soc. 52 (1975), 81-84 Request permission

Abstract:

All rings under consideration are Prüfer domains or valuation domains. We characterize the set of basic ideals and the set of $C$-ideals in an arbitrary valuation ring. Basic ideals were introduced in 1954 by Northcott and Rees. The concept of a $C$-ideal is, in a sense, directly opposite to that of a basic ideal. We then prove that a necessary and sufficient condition for every ideal in a domain $D$ to be basic is that $D$ be a one-dimensional Prüfer domain.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 81-84
  • MSC: Primary 13F05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0376655-2
  • MathSciNet review: 0376655