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Transactions of the American Mathematical Society

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Amalgamations of lattice ordered groups


Author: Keith R. Pierce
Journal: Trans. Amer. Math. Soc. 172 (1972), 249-260
MSC: Primary 06A55
DOI: https://doi.org/10.1090/S0002-9947-1972-0325488-3
MathSciNet review: 0325488
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Abstract: The author considers the problem of determining whether certain classes of lattice ordered groups ($ l$-groups) have the amalgamation property. It is shown that the classes of abelian totally ordered groups ($ o$-groups) and abelian $ l$-groups have the property, but that the class of $ l$-groups does not. However, under certain cardinality restrictions one can find an $ l$-group which is the ``product'' of $ l$-groups with an amalgamated subgroup whenever (a) the $ l$-subgroup is an Archimedian $ o$-group, or (b) the $ l$-subgroup is a direct product of Archimedian $ o$-groups and the $ l$-groups are representable. This yields a new proof that any $ l$-group is embeddable in a divisible $ l$-group, and implies that any $ l$-group is embeddable in an $ l$-group in which any two positive elements are conjugate.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0325488-3
Keywords: Amalgamation property, amalgams of lattice ordered groups, lattice ordered groups, totally ordered groups, extensions of lattice ordered groups
Article copyright: © Copyright 1972 American Mathematical Society

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