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l-simple lattice-ordered groups

Published online by Cambridge University Press:  20 January 2009

A. M. W. Glass
A. M. W. Glass
Affiliation:
Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.
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Let G be a lattice-ordered group (l-group) and H a subgroup of G. H is said to be an l-subgroup of G if it is a sublattice of G. H is said to be convex if h1, h2 ∈ H and h2 ≦ g ≦ h2 imply g ∈ H. The normal convex l-subgroups (l-ideals) of an l-group play the same role in the study of lattice-ordered groups as do normal subgroups in the investigation of groups. For this reason, an l-group is said to be l-simple if it has no non-trivial l-ideals. As in group theory, a central task in the examination of lattice-ordered groups is to characterise those l-groups which are l-simple.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 2 , September 1974 , pp. 133 - 138
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

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