Vol. 47, No. 2, 1973

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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

An l-ideal A of an l-group G is closed if x A whenever x = ai,0 ai 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
Received: 18 April 1972
Published: 1 August 1973
Roger Daniel Bleier
Paul F. Conrad