Frobenius homomorphism
Thus the map
is a field homomorphism, called the Frobenius homomorphism, or simply the Frobenius map on . If it is surjective then it is an automorphism, and is called the Frobenius automorphism.
Note: This morphism is sometimes also called the “small Frobenius” to distinguish it from the map , with . This map is then also referred to as the “big Frobenius” or the “power Frobenius map”.
Title | Frobenius homomorphism |
---|---|
Canonical name | FrobeniusHomomorphism |
Date of creation | 2013-03-22 12:22:50 |
Last modified on | 2013-03-22 12:22:50 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 11 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 12E99 |
Synonym | Frobenius endomorphism |
Synonym | Frobenius map |
Related topic | FrobeniusMorphism |
Related topic | FrobeniusMap |
Defines | Frobenius automorphism |