639: Units of Ring

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definition of units of ring

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Topics

About: ring

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description
• 3: Note

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Starting Context

• The reader knows a definition of ring.

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Target Context

• The reader will have a definition of units of ring.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$R$: $\in \{\text{ the rings }\}$
$\ast U$: $=\{u\in R|\mathrm{\exists }{u}^{-1}\in R(u{u}^{-1}=u^{-1}u=1)\}$, $\subseteq R$
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Conditions:
//

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2: Natural Language Description

For any ring, $R$, the subset, $U=\{u\in R|\mathrm{\exists }{u}^{-1}\in R(u{u}^{-1}=u^{-1}u=1)\}\subseteq R$

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3: Note

$1\in U$, but there can be some other units.

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References

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