A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN
This thesis deals with a class of complete modules over a discrete valuation domain. A module over a discrete valuation domain is said to be complete if it is Hausdorff and every Cauchy sequence of its elements is convergent. The class of complete modules over a discrete valuation domain can be iden...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/19067 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This thesis deals with a class of complete modules over a discrete valuation domain. A module over a discrete valuation domain is said to be complete if it is Hausdorff and every Cauchy sequence of its elements is convergent. The class of complete modules over a discrete valuation domain can be identified through its structure; particularly the structure of a pure-injective module and the height of elements. This thesis shows that any module <br />
<br />
<br />
<br />
<br />
is complete if and only if it is a pure-injective module having no infinite height elements. The result shows that all of complete modules are contained in a class of modules, that is reduced pure-injective modules class. Furthermore, it is also shown that if a pure submodule is complete then it is a direct summand. <br />
|
|---|