Vol. 47, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 327: 1
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
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