Generalized Commutativity of Lattice-Ordered Groups
-
M. R. Darnel
,
W. C. Holland
Abstract
In this paper we explore generalizations of Neumann’s theorem proving that weak commutativity in ordered groups actually implies the group is abelian. We show that a natural generalization of Neumann’s weak commutativity holds for certain Scrimger ℓ-groups.
References
[1] DARNEL, M. R.: Theory of Lattice-Ordered Groups, Marcel Dekker, New York, 1995.Suche in Google Scholar
[2] DARNEL, M. R.-HOLLAND,W. C.: Minimal non-metabelian varieties of ℓ-groups which contain no nonabelian o-groups, Comm. Algebra 42 (2014), 5100-5133.10.1080/00927872.2013.833209Suche in Google Scholar
[3] HOLLAND, W. C.: Intrinsic metrics for lattice-ordered groups, Algebra Universalis 19 (1984), 142-150.10.1007/BF01190425Suche in Google Scholar
[4] HOLLAND, W. C.-MEKLER, A.-REILLY, N.: Varieties of lattice-ordered groups in which prime powers commute, Algebra Universalis 23 (1986), 196-214.10.1007/BF01237720Suche in Google Scholar
[5] NEUMANN, B. H.: On ordered groups, Amer. J. Math. 71 (1949), 1-18.10.2307/2372087Suche in Google Scholar
[6] SMITH, J. E.: A new family of ℓ-group varieties, Houston J. Math. 7 (1981), 551-570. Suche in Google Scholar
© Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- 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
Artikel in diesem Heft
- 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
