Special-valued subgroups of lattice-ordered groups
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- by Yuanqian Chen and Paul Conrad PDF
- Proc. Amer. Math. Soc. 127 (1999), 1893-1902 Request permission
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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1476124