Some examples of hyperarchimedean l-groups
by
Anthony W. Hager
Wesleyan University
Coauthors: Chawne M. Kimber (Wesleyan University and Lafayette College)

An l-group is called hyperarchimedean if each of its quotients is archimedean.The basic paper is Conrad,1974.We consider such groups with a strong unit.Such G is exactly an intermediate between S(YG,Z) and C(YG) with G a-extending the former.( YG is the compact Hausdorff 0-dimensional space of maximal ideals,S(YG,Z) is the l-group of continuous Z-valued functions (which are Step functions),and an a-extension is one preserving the lattice of convex l-subgroups.) Following Conrad's fundamental example, we write down all G's for which YG is the convergent sequence;it becomes obvious which are a-closed.Pasting a lot of these together creates an a-closed G with a maximal ideal M with quotient not R.This solves a 1981 problem of Anderson and Conrad.Pasting a lot of these examples together creates a G with many such M.Such examples can be created also from a coproduct construction.(Still,questions remain.) Actually,G has all such quotients equal R iff G is "hyper-a-closed",and this occurs if G is a-closed with all points of YG zero-sets (but questions remain).We also characterize the hyperarchimedean products (in the strong-unit category).This creates interesting generalizations of singular l-groups,with other uses.

Date received: February 5, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caed-04.