definition of principal integral domain
Topics
About: ring
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 integral domain.
- The reader knows a definition of principal ideal of ring.
Target Context
- The reader will have a definition of principal integral domain.
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:
\(*R\): \(\in \{\text{ the integral domains }\}\)
//
Conditions:
\(\forall I \in \{\text{ the ideals of } R\} (I \in \{\text{ the principal ideals of } R\})\)
//
2: Natural Language Description
Any integral domain, \(R\), such that its each ideal is a principal ideal
3: Note
It is called also "Principal Ideal Domain". In fact, "Principal Ideal Integral Domain" will be more appropriate.
