Re: euclidean algorithm over Q[i]

In article <62tgh.6569$Dr3.1078@xxxxxxxxxxxxxxxxxxxx>, Jeremy Watts
<stevie4545@xxxxxxxxxxx> wrote:

how does the euclidean algorithm proceed for numbers in Q[i] ? my knowledge
of abstract algebra's basic to say the least so i hope i am using the
correct term. i mean for complex numbers with rational real & complex parts
ie. of form a/b + c/d i a,b,c,d in Z

i'm sure i have seen this somewhere but cant find reference to it anywhere.

thanks



Q[i] is a field, so greatest common divisors are easy.
Any nonzero element divides any other nonzero element.

Z[i], the Gaussian integers, may be what you remember seeing.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.