Partially ordered group
id:
partially-ordered-group-308-17334472
title:
Partially ordered group
text:
In abstract algebra, a partially ordered group is a group (G, +) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a + g ≤ b + g and g + a ≤ g + b. An element x of G is called positive if 0 ≤ x. The set of elements 0 ≤ x is often denoted with G+, and is called the positive cone of G. By translation invariance, we have a ≤ b if and only if 0 ≤ -a + b.
So we can reduce the partial order to a monadic p
brand slug:
wiki
category slug:
encyclopedia
description:
Group with a compatible partial order
original url:
https://en.wikipedia.org/wiki/Partially_ordered_group
date created:
date modified:
2024-04-01T11:18:10Z
main entity:
{"identifier":"Q2715875","url":"https://www.wikidata.org/entity/Q2715875"}
image:
fields total:
13
integrity:
14