Does it make sense to talk about the kernel of a field morphism? If so, what is it? I'm getting confused because we've defined a field to be a commutative group (F,+) and a map m: F -> F s.t. (F \{0}, m) form another commutative group. For shorthand we're calling the unit element for the + operation 0, and the unit element for m as 1.(adsbygoogle = window.adsbygoogle || []).push({});

So I'd want to define the kernel of a field morphism as the set of all elements in F1 that get mapped to 0 in F2, and the set of all element in F1 that get mapped to 1 in F2. Help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Kernel of a Field Morphism?

**Physics Forums | Science Articles, Homework Help, Discussion**