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The hulls of representable l-groups and f-rings

Published online by Cambridge University Press:  09 April 2009

Paul Conrad
Paul Conrad
Affiliation:
Department of MathematicsUniversity of KansasLawrence, Kansas 66044, U.S.A.
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A lattice-ordered group (“l-group”) G will be called

a P-group if G = g″ ⊕ g′ for each g ∈ G (projectable)

an SP-group if G = C ⊕ 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 385 - 415
Copyright
Copyright © Australian Mathematical Society 1973

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