Isomorphism between Q[x]/(x-1) and Q[x]/(x-2)

Palindrom · Dec 12, 2004

I really don't want to define a homomorphism like
psi(p(x))=p(x-1+I
I'm looking for another way to solve that next question:

Show that Q[x]/(x-1) is isomorphic to Q[x]/(x-2).
Any ideas?
Thanks in advance.

Hurkyl · Dec 12, 2004

You could show they're both isomorphic to a third ring...

Palindrom · Dec 12, 2004

Hurkyl said:

You could show they're both isomorphic to a third ring...

Of course, they're both isomorphic to Q... I really shouldn't do HW at 11 pm... Thanks!

Isomorphism between Q[x]/(x-1) and Q[x]/(x-2)

Discussion

Why does adiabatic compression use more energy than adiabatic expansion?

What force causes precession?

Simple kinematics problem — falling from a geostationary satellite

Why does a fan cool you in a sealed room if it adds heat?

If Heat Is Motion, Why Isn’t All Motion Heat?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Isomorphism between Q[x]/(x-1) and Q[x]/(x-2)

Discussion

Similar threads

Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

Undergrad Why is Q[x]/(x²-5) equal to Q[√5]?

Undergrad Why must an isomorphism between 2Z and 3Z result in mu(2) = +/- 3?

Graduate Is Q(√2) isomorphic to Q[X]/(X²-2)?