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Splitting properties in Archimedean l-groups

Published online by Cambridge University Press:  09 April 2009

Marlow Anderson ,
Paul Conrad  and
Otis Kenny
Marlow Anderson
Affiliation:
The University of Kansas, Lawrence, Kansas 66045, U.S.A.
Paul Conrad
Affiliation:
The University of Kansas, Lawrence, Kansas 66045, U.S.A.
Otis Kenny
Affiliation:
The University of Kansas, Lawrence, Kansas 66045, U.S.A.
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Throughout this paper an l-group will always mean an archimedean lattice-ordered group and we shall confine our attention to such groups. An l-group splits if it is a cardinal summand of each l-group that contains it as an l-ideal. Suppose that G is an l-subgroup of an l-group H. Then G is large in H or H is an essential extension of G if for each l-ideal L≠0 of H, L∩G≠0. G is essentially closed if it does not admit any proper essential extension. Conrad (1971) proved that each essentially closed l-group splits, but not conversely.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 2 , March 1977 , pp. 247 - 256
Copyright
Copyright © Australian Mathematical Society 1977

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