Characteristic of a field
A positive prime number or the number 0 that is uniquely determined for a given field in the following way. If for some ,
where is the unit element of the field , then the smallest such is a prime number; it is called the characteristic of . If there are no such numbers, then one says that the characteristic of is zero or that is a field of characteristic zero. Sometimes such a field is said to be without characteristic or of characteristic infinity . Every field of characteristic zero contains a subfield isomorphic to the field of all rational numbers, and a field of finite characteristic contains a subfield isomorphic to the field of residue classes modulo .
Characteristic of a field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_of_a_field&oldid=17329