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

DOI:
https://doi.org/10.1090/S0002-9939-99-04662-6

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 is the special-valued quasi-torsion radical of a lattice-ordered group , which extends our earlier result that the intersection of all maximal finite-valued subgroups of a lattice-ordered group is the finite-valued torsion radical of . We also show that the class of almost finite-valued lattice-ordered groups is a quasi-torsion class, and the 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:
https://doi.org/10.1090/S0002-9939-99-04662-6

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