1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gcd(a,b) unique in Euclidean domain?

  1. Apr 9, 2012 #1
    gcd(a,b) unique in Euclidean domain??

    1. The problem statement, all variables and given/known data
    In Hungerford's Algebra on page 142, the problem 13 describes Euclidean algorithm on a Euclidean domain R to find THE greatest common divisor of a,b in R.

    My question is that does this THE mean THE UNIUQE? I've heard from my lecturer in a general commutative ring, a greatest common divisor of a,b in R does not have to be unique.



    Is there any theorem such as states that if R is a Euclidean domain, then for any a,b in R, gcd(a,b) is unique?


    2. Relevant equations



    3. The attempt at a solution
    Sorry, I have not figured out at all...
     
  2. jcsd
  3. Apr 9, 2012 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: gcd(a,b) unique in Euclidean domain??

    It's not even unique in the integers: 5 and -5 are both greatest common divisors of 20 and 35, for example. However, there is a simple relationship between all of the possibilities for a gcd....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Gcd(a,b) unique in Euclidean domain?
Loading...