English, asked by aratikeche510, 4 months ago

what is the characteristic of field

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Answered by aamitarbhosale
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Explanation:

An invariant of a field which is either a prime number or the number zero, uniquely determined for a given field in the following way. If for some n>0

0= ne= e+e+e+.........+e

where e is the unit element of the field F, then the smallest such n is a prime number; it is called the characteristic of F. If there are no such numbers n, then one says that the characteristic of F is zero or that F 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 p contains a subfield isomorphic to the field of residue classes modulo p: in each case this is the prime field.

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