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.References
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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