Results 281 to 290 of about 309,890 (334)
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Algebra and Logic, 1995
The author proves that any Engel lattice-ordered group (\(l\)-group) which generates a proper normal-valued variety of \(l\)-groups is \(o\)-approximable and that the Engel \(l\)-groups from any proper normal-valued variety of \(l\)-groups form a torsion class.
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The author proves that any Engel lattice-ordered group (\(l\)-group) which generates a proper normal-valued variety of \(l\)-groups is \(o\)-approximable and that the Engel \(l\)-groups from any proper normal-valued variety of \(l\)-groups form a torsion class.
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2009
In this chapter we present the most basic parts of the theory of lattice-ordered groups. Though our main concern will eventually be with abelian groups it is not appreciably harder to develop this material within the class of all groups. Moreover, the additional generality allows us to digress somewhat (if it is possible to digress before one begins ...
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In this chapter we present the most basic parts of the theory of lattice-ordered groups. Though our main concern will eventually be with abelian groups it is not appreciably harder to develop this material within the class of all groups. Moreover, the additional generality allows us to digress somewhat (if it is possible to digress before one begins ...
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Algebra and Logic, 1979
Let \(F_ r\) be the free lattice ordered group of finite rank \(r\geq 2\). A representation is obtained for \(F_ r\) as an \(\ell\)-subgroup of the \(\ell\)-group of all o-permutations of the real line. Using this representation the author proves the following.
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Let \(F_ r\) be the free lattice ordered group of finite rank \(r\geq 2\). A representation is obtained for \(F_ r\) as an \(\ell\)-subgroup of the \(\ell\)-group of all o-permutations of the real line. Using this representation the author proves the following.
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Disjointifiable lattice-ordered groups
Algebra universalis, 2008This article studies disjointifiable lattice-ordered groups (abbr. dl-groups): the lattice-ordered groups G for which the frame \({\mathcal{C}}(G)\) of all convex l-subgroups is a normal frame; that is, for which \(A {\vee} B = G {\rm in} \mathcal{C}(G)\) implies the existence of \(C, D {\in} \,{\mathcal{C}}(G)\) such that C ⋂D = 0 and A ∨ D = C ∨ B ...
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Nilpotent lattice-ordered groups
Mathematical Notes of the Academy of Sciences of the USSR, 1989See the review in Zbl 0681.06006.
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Frolík decompositions for lattice-ordered groups
Quaestiones Mathematicae, 2017Frolik's theorem says that a homeomorphism from a certain kind of topological space to itself decomposes the space into the clopen set of xed points together with three clopen sets, each of whose images is disjoint from the original set. Stone's theorem translates this result to a corresponding theorem about the Riesz space of continuous functions on ...
Buskes, Gerard, Redfield, R.H.
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Countable lattice-ordered groups
Mathematical Proceedings of the Cambridge Philosophical Society, 1983A lattice-ordered group is a group and a lattice such that the group operation distributes through the lattice operations (i.e. f(g ∨ h)k = fgk ∨ fhk and dually). Lattice-ordered groups are torsion-free groups and distributive lattices. They further satisfy f ∧ g = (f−1 ∨ g−1)−1 and f ∨ g = (f−1 ∧ g−1)−1. Since the lattice is distributive, each lattice-
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Nilpotent lattice-ordered groups
Algebra Universalis, 1979A lattice-ordered groupG isweakly abelian if for each ...
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Lattice-Ordered Permutation Groups
1989Although most of the elementary theorems about o-groups are as easy to prove in the general case as in the commutative case, there are no natural examples of non-commutative o-groups. Of course, it is easy to construct examples of non-commutative o-groups, but all of these are artificial and without much interest outside of the context of ordered ...
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1989
The definition of the free lattice-ordered group Fη of a given rank η is analogous to that of the free group Gη. Yet there are many questions which have the same “obvious” answers in both contexts, and for which the answers are very easy to confirm for free groups but not at all easy for free l-groups. We assume η > 1. Some questions: 1. Does Fη
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The definition of the free lattice-ordered group Fη of a given rank η is analogous to that of the free group Gη. Yet there are many questions which have the same “obvious” answers in both contexts, and for which the answers are very easy to confirm for free groups but not at all easy for free l-groups. We assume η > 1. Some questions: 1. Does Fη
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