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