prime subfield
The prime subfield of a field F is the intersection of all subfields
of F, or equivalently the smallest subfield of F. It can also be constructed by taking the quotient field of the additive subgroup
of F generated by the multiplicative identity
1.
If F has characteristic p where p>0 is a prime, then the prime subfield of F is isomorphic
to the field ℤ/pℤ of integers mod p. When F has characteristic zero, the prime subfield of F is isomorphic to the field ℚ 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 |