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The relatively uniform completion, epimorphisms and units, in divisible archimedean $l$-groups

In: Mathematica Slovaca, vol. 65, no. 2
Anthony W. Hager

Details:

Year, pages: 2015, 343 - 358
Keywords:
lattice-ordered group, archimedean, relatively uniform completion, weak order unit, near unit, epimorphism
About article:
In the category Arch of archimedean $l$-groups, the r.u. completion of the divisible hull, $rdA$, is the maximum essential reflection and the maximum majorizing reflection (Ball-Hager, 1999). In the weak-unital subcategory $W$, the reflections $c3A$ and $mA$ (Aron-Hager, 1981) are respectively maximum essential, and maximum majorizing (Ball-Hager, 1993), and $rdA ≤ mA$ always. These situations are reviewed here, and further, it is shown that: $W$-epic $A ≤ B$ is Arch-epic if the unit of $B$ is a near unit; $rdA = mA$ if and only if $A ≤ mA$ is Arch-epic, and this obtains when the unit of $A$ is a near unit. (If $A \in W$ has a compatible $f$-ring multiplication, then the unit (the identity) is a near unit.) A point here is that $mA$ has a concrete and understandable description as real-valued functions on the Yosida space of $A$, perforce, when $rdA = mA$ so does $rdA$.
How to cite:
ISO 690:
Hager, A. 2015. The relatively uniform completion, epimorphisms and units, in divisible archimedean $l$-groups. In Mathematica Slovaca, vol. 65, no.2, pp. 343-358. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0027

APA:
Hager, A. (2015). The relatively uniform completion, epimorphisms and units, in divisible archimedean $l$-groups. Mathematica Slovaca, 65(2), 343-358. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0027
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