prime subfield

The prime subfieldMathworldPlanetmath of a field F is the intersection of all subfieldsMathworldPlanetmath of F, or equivalently the smallest subfield of F. It can also be constructed by taking the quotient field of the additive subgroupMathworldPlanetmathPlanetmath of F generated by the multiplicative identityPlanetmathPlanetmath 1.

If F has characteristicPlanetmathPlanetmath p where p>0 is a prime, then the prime subfield of F is isomorphicPlanetmathPlanetmathPlanetmath to the field /p of integers mod p. When F has characteristic zero, the prime subfield of F is isomorphic to the field of rational numbers.

Title prime subfield
Canonical name PrimeSubfield
Date of creation 2013-03-22 12:37:47
Last modified on 2013-03-22 12:37:47
Owner djao (24)
Last modified by djao (24)
Numerical id 4
Author djao (24)
Entry type Definition
Classification msc 12E99