Let R be an integral domain and r, s $\in$ R.
I know that an integral domain is a commutative ring with identity that has no zero-divisors. Hence, R is a commutative ring with identity and has no zero-divisors.
Given this, can the gcd(r, s) have more than one gcd? Also, would the gcd(r, s) be associates of one another?
I am trying to work this out in $\mathbb{Z}$[$x$] (since I know that $\mathbb{Z}$ is an integral domain as $\mathbb{Z}$[$x$] is a commutative polynomial ring with identity that has no zero-divisors) but I do not know if this is a smart integral domain to work with. Would appreciate some guidance. Thanks in advance