Lattice-ordered groups and a conjecture for adequate domains
Authors:
J. W. Brewer, P. F. Conrad and P. R. Montgomery
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
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Abstract | References | Similar Articles | Additional Information
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 
-groups are false.
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-extensions of an abelian 
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0332616-X
Keywords:
Lattice ordered abelian group,
adequate domain,
group of divisibility,
elementary divisor ring,
lateral completion
Article copyright:
© Copyright 1974
American Mathematical Society
