CHARACTERIZATION A FINITELY GENERATED DEDEKIND MODULES OVER ORDER MODULE
Let R be a commutative ring with unity and T be the multiplicative set of all regular elements in R. A fraction ring of R, can be constructed such that R can be embedded into RT (-1). One of the relation between a ring and a module is given by an order of the module 0(M). The order of the module...
Saved in:
| Main Author: | |
|---|---|
| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/34873 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let R be a commutative ring with unity and T be the multiplicative set of all
regular elements in R. A fraction ring of R, can be constructed such that R
can be embedded into RT (-1). One of the relation between a ring and a module
is given by an order of the module 0(M). The order of the module is known
as a commutative ring. Moreover, it is a subring of a fraction ring. A ring
whose every non-zero ideal is invertible called a Dedekind ring. The concept
of an invertible ideal in a ring will be generated into a module theory. In a
module theory, its already developed the concept of an invertible submodule.
Therefore, a Dedekind module can be defined. Studying relation between M
as an R-module and as a 0(M)-module gives that the properties of M as a
0(M)-module can be identified from M as an R-module. A 0(M)-module will
be known as a Dedekind module, the order of M will be a Dedekind ring and
it is an integrally closed if M is a finitely generated Dedekind R-module. The
main result is studying about characteristics of a finitely generated Dedekind
module related to the properties of the order of modules. |
|---|