Editing Characteristic (algebra) (section)

{{Short description|Smallest integer n for which n equals 0 in a ring}}

In [[mathematics]], the '''characteristic''' of a [[ring (mathematics)|ring]] {{math|''R''}}, often denoted {{math|char(''R'')}}, is defined to be the smallest positive number of copies of the ring's [[identity element|multiplicative identity]] ({{math|1}}) that will sum to the [[additive identity]] ({{math|0}}). If no such number exists, the ring is said to have characteristic zero. 

That is, {{math|char(''R'')}} is the smallest positive number {{math|''n''}} such that:<ref name=Fraleigh-Brand-2020/>{{rp|style=ama|p= 198, Thm. 23.14}} 
: <math>\underbrace{1+\cdots+1}_{n \text{ summands}} = 0</math>
if such a number {{math|''n''}} exists, and {{math|0}} otherwise.