The lattice of closed ideals and a^∗-extensions of an abelian l-group

Roger Daniel Bleier and Paul F. Conrad

Vol. 47 (1973), No. 2, 329–340

DOI: 10.2140/pjm.1973.47.329

Abstract

An l-ideal A of an l-group G is closed if x ∈ A whenever x = ∨a_i,0 ≤ a_i ∈ A. The intersection of any collection of closed l-ideals of G is again a closed l-ideal of G. Hence the set 𝒦(G) of all closed l-ideals of G is a complete lattice under inclusion. In the present paper this lattice is studied, as well as l-group extensions which preserve it. A common generalization of the essential closure of an archimedean l-group and the Hahn closure of a totally-ordered abelian group is obtained.

Mathematical Subject Classification

Primary: 06A55

Milestones

Received: 18 April 1972

Published: 1 August 1973