Frames associated with an abelian 𝑙-group

Madden, James J.

doi:10.1090/S0002-9947-1992-1042288-2

Frames associated with an abelian $l$-group
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Trans. Amer. Math. Soc. 331 (1992), 265-279 Request permission

Abstract:

Every archimedean $l$-group (lattice-ordered group) with weak unit is shown to be isomorphic to a sub-$l$-group of the $l$-group of continuous realvalued functions on a Tychonoff locale canonically associated with the $l$-group. This strengthens the classical Yosida representation theorem in a useful way. The proof uses methods from universal algebra and is constructive.

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A syntactic construction of the spectrum of a commutative