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

Ball, Richard N.; Hager, Anthony W.; Kizanis, Ann

doi:10.1090/S0002-9939-1992-1100643-1

Epimorphic adjunction of a weak order unit to an Archimedean lattice-ordered group
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by Richard N. Ball, Anthony W. Hager and Ann Kizanis PDF

Proc. Amer. Math. Soc. 116 (1992), 297-303 Request permission

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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Epicompletions of archimedean lattice-ordered groups

Riesz spaces