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Complementing lattice-ordered groups: The finite-valued case

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Abstract

A complementedl-groupG is one in which to eacha εG there exists ab εG so that¦a¦ λ ¦b¦=0, while¦a¦ ∀ ¦b¦ is a unit ofG. IfG is anl-subgroup ofH, and the latter is complemented, then we say thatH is a complementation ofG ifG c, the convex hull ofG inH, is a strongly rigid extension ofG andG c is az-subgroup ofH. This article presents necessary and sufficient conditions for a finite-valuedl-subgroup to admit a complementation.

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  1. Department of Mathematics, University of Florida, 32611, Gainesville, Florida, USA

    J. Martinez

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  1. J. Martinez
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Martinez, J. Complementing lattice-ordered groups: The finite-valued case. Algebra Universalis 33, 243–253 (1995). https://doi.org/10.1007/BF01190936

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