|
|
|
|
|
Linearly Ordered GroupIn mathematics, a linearly ordered group is both a group and a linearly ordered set, in which the group operation is in a certain sense compatible with the linear ordering. Specifically, we have - For any x in the group G, either x ≥ 0 or −x ≥ 0, but not both, and
- For any x, y, z in G, if x ≤ y, then x + z ≤ y + z.
(See also ordered group.) Otto Hölder showed that every linearly ordered group satisfying an Archimedean property is isomorphic to a subgroup of the additive group of real numbers.
|
 |
|
| Copyright 2005-2009 OnPedia.com. All Rights Reserved |
|
|