Explore BrainMass
Share

Isomorphisms Described

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

f(x)=x^3+x+1 and g(x)=x^3+x^2+1 are irreducible over F_2. K is the field extension obtained by adjoining a root of f and L is the extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism)

© BrainMass Inc. brainmass.com March 21, 2019, 11:40 pm ad1c9bdddf
https://brainmass.com/math/linear-transformation/isomorphisms-described-468637

Attachments

Solution Preview

f(x)=x^3+x+1 and g(x)=x^3+x^2+1 are irreducible over F_2. K is the field extension obtained by adjoining a root of f and L is the extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism)

Solution: Let K=F_2 (α), where α is a root of f(x)=x^3+x+1.
Now ...

Solution Summary

The expert determines the number of isomorphism from K to L.

$2.19