definition of units of ring
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 ring.
Target Context
- The reader will have a definition of units of ring.
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:
\( R\): \(\in \{\text{ the rings }\}\)
\(*U\): \(= \{u \in R \vert \exists u^{-1} \in R (u u^{-1} = u^{-1} u = 1)\}\), \(\subseteq R\)
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Conditions:
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2: Natural Language Description
For any ring, \(R\), the subset, \(U = \{u \in R \vert \exists u^{-1} \in R (u u^{-1} = u^{-1} u = 1)\} \subseteq R\)
3: Note
\(1 \in U\), but there can be some other units.
