Journal of the Australian Mathematical Society

Table of Contents - 1973 - Volume 16, Issue 04  

Research Article

The hulls of representable l-groups and f-rings

Paul Conrada1

a1 Department of Mathematics University of Kansas Lawrence, Kansas 66044, U.S.A.

A lattice-ordered group (“l-group”) G will be called

a P-group if G = g″ xs2295 g′ for each g xs2208 G (projectable)

an SP-group if G = C xs2295 C′ for each polar C of G (strongly projectable)

an L-group if each disjoint subset has a 1. u. b. (laterally complete)

an O group if it is both an L-group and a P-group (orthocomplete).

G is representable if it is an l-subgroup of a cardinal product of totally ordered groups. It follows that a P-group must be representable and hence SP-groups and O-groups are also representable.

(Received September 11 1971)