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2013 *-Maximum lattice-ordered groups
Anthony W. Hager
Rocky Mountain J. Math. 43(6): 1901-1930 (2013). DOI: 10.1216/RMJ-2013-43-6-1901

Abstract

The category $W$ is archimedean $l$-groups $G$ with distinguished weak order unit $e_G$, with unit-preserving $l$-group homomorphisms. For $G$ in $W$, $G^*$ denotes the convex sub-$l$-group generated by $e_G$. If $G$ satisfies [any isomorphism of $H^*$ with $G^*$ extends to an embedding of $H$ in $G$], then $G$ is called $\ast$-maximum. ($H^*$ and $G^*$ are isomorphic if and only if the unit intervals $[0, e_H]$ and $[0, e_G]$ are isomorphic MV-algebras.) This paper analyzes the property ``$\ast$-maximum'': Several characterizations are given. It is shown that any $\ast$-maximum $G$ has quasi-F Yosida space; this applies to prove a conjecture of the author and J\. Martinez about ``rings of $\omega_1$-quotients.'' It is shown that each $G$ in $W$ has a $\ast$-maximum hull, and this hull is described.

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Anthony W. Hager. "*-Maximum lattice-ordered groups." Rocky Mountain J. Math. 43 (6) 1901 - 1930, 2013. https://doi.org/10.1216/RMJ-2013-43-6-1901

Information

Published: 2013
First available in Project Euclid: 25 February 2014

zbMATH: 1309.06010
MathSciNet: MR3178449
Digital Object Identifier: 10.1216/RMJ-2013-43-6-1901

Subjects:
Primary: 06F20, 46E05, 54G05
Secondary: 03B50, 18A40, ‎54C30

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.43 • No. 6 • 2013
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