Note that the first definition also applies to arbitrary rings, and not just to fields.
The characteristic of a field (or more generally an integral domain) is always prime. For if the characteristic of were composite, say for , then in particular would equal zero. Then either would be zero or would be zero, so the characteristic of would actually be smaller than , contradicting the minimality condition.
|Date of creation||2013-03-22 12:05:01|
|Last modified on||2013-03-22 12:05:01|
|Last modified by||Mathprof (13753)|