ENDOMORPHISM RINGS OF FINITELY GENERATED MODULES OVER A PRINCIPAL IDEAL DOMAIN
This thesis deals with an identication of endomorphism rings of nitely generated modules over a principal ideal domain with matrix rings. A fact that will be used is that a nitely generated module over a principal ideal domain can be decomposed into a direct sum of its torsion submodule and a fre...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/44566 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This thesis deals with an identication of endomorphism rings of nitely generated modules
over a principal ideal domain with matrix rings. A fact that will be used is that a nitely
generated module over a principal ideal domain can be decomposed into a direct sum of
its torsion submodule and a free submodule. Furthermore, the torsion submodule can be
decomposed into a direct sum of primary submodules and each primary submodules can be
decomposed into a direct sum of cyclic submodules. On the other hand, the free submodule
can be decomposed into a direct sum of cyclic submodules generated by elements in its
basis. In this thesis, it is shown that the endomorphism rings of nitely generated modules
over a principal ideal domain can be identied by a 2 2 upper block matrix ring where
block-(11) represents the endomorphism ring of torsion submodule, block-(12) represents
the homomorphism module from the free submodule to the torsion submodule, and block-
(22) represents the endomorphism ring of free submodule. Details of each block is also
presented in this thesis. |
|---|