On lattice property of group induced cone orderings
β Scribed by Marek Niezgoda
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 102 KB
- Volume
- 307
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
β¦ Synopsis
The problem of existence and uniqueness of greatest lower bound (glb) and least upper bound (lub) of a set in group induced cone (GIC) ordering is discussed. Explicit formula for the glb is given. The results are applied to obtain the best possible upper bound in GIC ordering for values of linear and nonnegative linear maps.
π SIMILAR VOLUMES
## An analytical characterization of effective and of irreducible groups inducing cone orderings is given. The characterization implies easily a necessary condition for a group majorization to be a group induced cone ordering.
In this paper, we introduce the concept of a valuation mapping of an l-group G onto a distributive lattice and use such valuations to investigate the structure of G. Then we examine the maximal immediate extensions of G with respect to these Ε½ valuations. For the natural valuation, these are the arc