Small Varieties of Lattice-Ordered Groups
by
W. Charles Holland
Bowling Green State Unversity, Emeritus

A lattice-ordered group is both a group and a lattice whose lattice operations are preserved by the group translations. A variety is the class of all lattice-ordered groups defined by any given set of universally quantified equations. The unique minimal nontrivial variety is the abelian variety. Because it is defined by the single equation xy = yx, there is a set of varieties covering the abelian variety. We will discuss these covers and point out some open questions concerning them. We will also note that this has interesting implications for varieties of generalized (non-commutative) MV-algebras.

Date received: May 19, 2004