Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
-
Jan Jákubík
and
Judita Lihoyá
Abstract
The notion of torsion radical of cyclically ordered groups is defined analogously as in the case of lattice ordered groups. We denote by T the collection of all torsion radicals of cyclically ordered groups. For τ1, τ2 ∈ T, we put τ1 ∈ τ2 if τ1(G) □ τ2(G) for each cyclically ordered group G. We show that T is a proper class; nevertheless, we apply for T the usual terminology of the theory of partially ordered sets. We prove that T is a complete completely distributive lattice. The analogous result fails to be valid for torsion radicals of lattice ordered groups. Further, we deal with products of torsion classes of cyclically ordered groups.
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Articles in the same Issue
- Complexities of Relational Structures
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- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
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Articles in the same Issue
- Complexities of Relational Structures
- Notes on the Product of Locales
- Free Objects and Free Extensions in the Category of Frames
- More on Uniform Paracompactness in Pointfree Topology
- Nonmeasurable Cardinals and Pointfree Topology
- Pseudocompact σ-Frames
- Torsion Radicals and Torsion Classes of Cyclically Ordered Groups
- Generalized Commutativity of Lattice-Ordered Groups
- The Relatively Uniform Completion, Epimorphisms and Units, in Divisible Archimedean L-Groups
- Polymorphism-Homogeneous Monounary Algebras
- αcc-Baer Rings
- Pushout Invariance Revisited
- Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models
