Difference between revisions of "Characteristic of a ring"
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* If {{M|\exists n\in\mathbb{N}_{\ge 0} }} such that {{M|\forall a\in R}} we have {{M|1=na=0}} then the smallest such integer {{M|n}} is the ''characteristic of {{M|R}}'' | * If {{M|\exists n\in\mathbb{N}_{\ge 0} }} such that {{M|\forall a\in R}} we have {{M|1=na=0}} then the smallest such integer {{M|n}} is the ''characteristic of {{M|R}}'' | ||
* If {{M|\nexists}} such an {{M|n}} we say {{M|R}} has ''characteristic 0'' | * If {{M|\nexists}} such an {{M|n}} we say {{M|R}} has ''characteristic 0'' | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
{{Definition|Abstract Algebra}} | {{Definition|Abstract Algebra}} | ||
Latest revision as of 18:52, 28 August 2015
Definition
Let [ilmath]R[/ilmath] be a ring. The characteristic of a ring is defined as follows[1]:
- If [ilmath]\exists n\in\mathbb{N}_{\ge 0} [/ilmath] such that [ilmath]\forall a\in R[/ilmath] we have [ilmath]na=0[/ilmath] then the smallest such integer [ilmath]n[/ilmath] is the characteristic of [ilmath]R[/ilmath]
- If [ilmath]\nexists[/ilmath] such an [ilmath]n[/ilmath] we say [ilmath]R[/ilmath] has characteristic 0
References
- ↑ Fundamentals of Abstract Algebra - Neal H. McCoy
