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In [[algebra]], the '''characteristic''' of a [[ring (mathematics)|ring]] ''R'' is the least [[natural number]] ''n'' such that, for all ''r'' in ''R'', ''n'' * ''r'' = 0. If no such natural number exists, the ring has characteristic 0.
In [[algebra]], the '''characteristic''' of a [[ring (mathematics)|ring]] ''R'' is the least [[natural number]] ''n'' such that, for all ''r'' in ''R'', ''n'' * ''r'' = 0. If no such natural number exists, the ring has characteristic 0.
==Examples==
*<math>(\mathbb{Z},+, \cdot)</math> - the set of the integers - has characteristic 0.
*<math>(\mathbb{Z} / 6\mathbb{Z},+, \cdot)</math> has characteristic 6:
:{|
|-
|0 ||= 0||=||0+0+0+0+0+0
|-
|1+1+1+1+1+1 ||= 0||=|| 1+1+1+1+1+1
|-
|2+2+2 ||= 0||=|| 2+2+2+2+2+2
|-
|3+3 ||= 0||=|| 3+3+3+3+3+3
|-
|4+4+4 ||= 0||=|| 4+4+4+4+4+4
|-
|5+5+5+5+5+5 ||= 0||=|| 5+5+5+5+5+5
|}