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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Special-valued subgroups
of lattice-ordered groups


Authors: Yuanqian Chen and Paul Conrad
Journal: Proc. Amer. Math. Soc. 127 (1999), 1893-1902
MSC (1991): Primary 06F15, 06F20; Secondary 20F60
Published electronically: February 26, 1999
MathSciNet review: 1476124
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the intersection of all maximal special-valued subgroups of a lattice-ordered group $G$ is the special-valued quasi-torsion radical of a lattice-ordered group $G$, which extends our earlier result that the intersection of all maximal finite-valued subgroups of a lattice-ordered group $G$ is the finite-valued torsion radical of $G$. We also show that the class $A_f$ of almost finite-valued lattice-ordered groups is a quasi-torsion class, and the $A_f$ quasi-torsion radical of a group is equal to the intersection of the group with the lateral completion of the finite-valued torsion radical of the group.


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Additional Information

Yuanqian Chen
Affiliation: Department of Mathematical Sciences, Central Connecticut State University, New Britain, Connecticut 06050
Email: chen@ccsua.ctstateu.edu

Paul Conrad
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04662-6
PII: S 0002-9939(99)04662-6
Keywords: Torsion class and quasi-torsion class, finite-valued and special-valued subgroups of a lattice-ordered group
Received by editor(s): July 16, 1996
Received by editor(s) in revised form: September 2, 1997
Published electronically: February 26, 1999
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society