ON QUASI-VARIETIES OF LATTICE ORDERED GROUPS GENERATED BY CYCLIC EXTENSIONS

Scope and Method of Study. This dissertation investigates several theorems in the study of lattice-ordered groups. The first theorem shows the existence of infinite chains of distinct quasi-varieties containing A and contained in the intersection of the variety of representable L-groups R and A('2). The second shows the existence of an infinite chain of distinct quasi-varieties between A and the intersection of the variety, L(,n) defined by x('n), y('n) = 1 and A('2). The third proves that every quasi-variety of L-groups constructed in the first case fails the amalgamation property, and the last shows that every quasi-variety of L-groups constructed in the second case fails the amalgamation property. This is intended for graduate students and research mathematicians who are interested in quasi-varieties of lattice ordered groups.;Findings and Conclusions. The quasi-varieties constructed show that the failure of the amalgamation property in classes of L-groups occurs much closer to the variety of abelian L-groups than was previously known.