The gcd of powers in a gcd domain

$\def\gcd{\operatorname{gcd}}$Let $R$ be a gcd domain. Does it always hold that $\gcd(x^m,y^m)=\gcd(x,y)^m$?

If the ring is a Bezout domain, then we can apply this method. However, a gcd domain may not be a Bezout domain. I don't know how I can go on.

is a duplicate

This question has been asked before and has already been answered. It should be marked as a duplicate.

Please enter the URL of the proposed duplicate in the details field below.

not constructive

This question cannot be answered in a way that is helpful to anyone. It's not possible to learn something from possible answers, except for the solution for the specific problem of the asker.

Communities

The gcd of powers in a gcd domain

0 comment threads

0 answers