VALUATIONS ON VECTOR SPACES AS A GENERALIZATION OF VALUATIONS ON FIELDS
This dissertation deals with valuations on vector spaces as a generalization of valuations on fields. The resulting contribution is formulation the concept of valuations <br /> <br /> <br /> on vector spaces as a generalization of valuations on fields. <br /> <br />...
Saved in:
| Main Author: | |
|---|---|
| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/24360 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This dissertation deals with valuations on vector spaces as a generalization of valuations on fields. The resulting contribution is formulation the concept of valuations <br />
<br />
<br />
on vector spaces as a generalization of valuations on fields. <br />
<br />
<br />
The main result of the dissertation is an interrelation between valuation modules and valuations on vector spaces. This result obtained as a generalization of the <br />
<br />
<br />
similar study in ring theory. This study is restricted to the class of torsion-free reduced modules. <br />
<br />
<br />
In the next discussion, it is shown that it can be constructed a topology on a reduced valuation module using the corresponding valuation on the module. As <br />
<br />
<br />
a result, every reduced valuation module is a topological module. Further, we use the results to study the completion of valuation modules. Particularly, investigated the completion of torsion-free reduced modules over discrete valuation rings. |
|---|