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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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Lattice-ordered groups and a conjecture for adequate domains
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by J. W. Brewer, P. F. Conrad and P. R. Montgomery PDF
Proc. Amer. Math. Soc. 43 (1974), 31-35 Request permission

Abstract:

In this paper, we present a counterexample to show that adequate domains are not characterized by the property that nonzero prime ideals are contained in a unique maximal ideal. The counterexample is obtained by constructing a lattice-ordered group with certain properties and exploiting the relation between Bezout domains and their (lattice-ordered) group of divisibility. The domain constructed is an elementary divisor ring with zero Jacobson radical. The lattice-ordered group constructed also shows that various conjectures about $l$-groups are false.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 31-35
  • MSC: Primary 06A60; Secondary 13F15
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0332616-X
  • MathSciNet review: 0332616