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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Epimorphic adjunction of a weak order unit to an Archimedean lattice-ordered group


Authors: Richard N. Ball, Anthony W. Hager and Ann Kizanis
Journal: Proc. Amer. Math. Soc. 116 (1992), 297-303
MSC: Primary 06F20; Secondary 18A20, 46A40
MathSciNet review: 1100643
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Abstract: It is shown that an archimedean $ l$-group $ G$ can be embedded into another, $ H$, which has a weak unit, by an embedding that is epimorphic in archimedean $ l$-groups if and only if there is countable $ A \subseteq G$ with $ {A^ \bot } = (0)$. Then the extension $ H$ can always be chosen conditionally and laterally $ \sigma $-complete and the embedding essential, but can never be generated by $ G$ together with finitely many extra elements unless $ G$ already had a weak unit.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1100643-1
PII: S 0002-9939(1992)1100643-1
Keywords: Archimedean $ l$-group, epimorphism, weak unit, coessential embedding
Article copyright: © Copyright 1992 American Mathematical Society