An ordered group is a group with a (partial) order which the group operation preserves.
An ordered group is a group with a (partial) order which the group operation preserves. For more information, see this Wikipedia article.
Questions tagged [ordered-groups]
68 questions
3
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Existence of a sequence converging to $0$
Let $(G,+,\le)$ be a partially ordered group (with identity $0$) and suppose that for each positive $g \in G$ there exists $g^\prime \in G$ such that $0
Paolo Leonetti
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Atoms of the Lattice of $\ell$-ideals of a lattice ordered group
I'm new to lattice groups and I'm stuck in the very first proposition (2.1) of Paul Conrad's paper "Characteristic Subgroups of Lattice-Ordered Groups" (http://www.jstor.org/stable/1995910). Part (c) of the statement says that
"If $A$ is an atom of…
Chrystomath
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Property of ordered groups.
A totally ordered abelian group is an abelian group (G,+) with a total order $\leq$ such that for all $a,b,c \in G$ if $a \leq b$ then $a+c \leq b+c$.
We will say that an ordered abelian group is dense in itself if for all $a
HeMan
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