Vector lattices on a set of two generators

It is proved that the center of an automorphism group Aut(FV L2) of a free vector lattice FV L2 on a set of two free generators is isomorphic to a multiplicative group of positive reals. It is shown that the free vector lattice FV L2 has an isomorphic representation by continuous piecewise linear functions of the real line; as a consequence, the ideal lattice and the root system for rectifying ideals in FV L2 are amply described. Similar results are obtained for a free vector lattice FV LQ2 generated by two elements over a field of rational numbers. © 2002 Plenum Publishing Corporation.