R is an Integral Domain.

Let c be a greatest common divisor of a and b in R and let f be an associate of c. Show that f is also a greatest common divisor of a and b in R.

Thoughts...

I think i should show that c|f and f|c. Then f would be the gcd as well.

f = uc, where u is a unit, so c|f. Can find another unit v R s.t. uv. = 1 (i.e. v is the inverse of u).

Then c = vf, hence f|c. So f is gcd as well?

On second thoughts, since R is an Int Domain maybe im not allowed to assume that uv = 1...