Explore BrainMass
Share

Fields and homomorphisms

This content was STOLEN from BrainMass.com - View the original, and get the solution, here!

Not sure why, but I am having trouble with this one. I'd really appreciate it if someone is willing to help here. Please see the attached file.

Thank you

© BrainMass Inc. brainmass.com September 20, 2018, 12:27 pm ad1c9bdddf - https://brainmass.com/math/linear-transformation/fields-homomorphisms-171539

Attachments

Solution Preview

Please see the attachment.

Proof:
(a) I define as , where and is a root of .
First, I claim that this mapping is well-defined.
Consider , then . Since , then . Then we have
.
So is well-defined.
Second, I claim that is a ...

Solution Summary

This provides an example of working with irreducible polynomials, fields, and homomorphisms.

$2.19