definition of finitely-generated module
Topics
About: module
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
- 3: Note
Starting Context
- The reader knows a definition of generator of module.
Target Context
- The reader will have a definition of finitely-generated module.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( R\): \(\in \{\text{ the rings }\}\)
\(*M\): \(\in \{\text{ the modules over } R\}\)
//
Conditions:
\(\exists S \in \{\text{ the finite generators of } M\}\)
//
2: Natural Language Description
For any ring, \(R\), any module, \(M\), that has a finite generator
3: Note
Being finitely-generated does not imply having any basis: see Note of the definition of generator of module.
