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Preprint Number 1479
1479. Almudena Colacito and George Metcalfe Ordering groups and validity in lattice-ordered groups E-mail: Submission date: 7 September 2018 Abstract: A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered groups (l-groups) to subsets of free groups that extend to positive cones of right orders. This correspondence is used to obtain new proofs of the decidability of the word problem for free l-groups and generation of the variety of l-groups by the l-group of automorphisms of the real number line. A characterization of the subsets of a group that extend to the positive cone of an order on the group is also used to establish a correspondence between the validity of equations in varieties of representable l-groups (equivalently, classes of ordered groups) and subsets of relatively free groups that extend to positive cones of orders. Mathematics Subject Classification: Keywords and phrases: |
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