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Ordering Groups and Validity in Lattice-ordered Groups by Colacito, Almudena; Metcalfe, George is a scholarly article available to read on EtoBox.

What is Ordering Groups and Validity in Lattice-ordered Groups about?

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.

Author

Colacito, Almudena; Metcalfe, George

Published

2018

Language

EN