In mathematics, a GCD domain is an integral domain R with the property that any two non-zero elements have a greatest common divisor (GCD). Equivalently, any two non-zero elements of R have a least common multiple (LCM).
A GCD domain generalizes a unique factorization domain to the non-Noetherian setting in the following sense: an integral domain is a UFD if and only if it is a GCD domain satisfying the ascending chain condition on principal ideals (and in particular if it is Noetherian).
Read more about GCD Domain: Properties, Examples
Famous quotes containing the word domain:
“You are the harvest and not the reaper
And of your domain another is the keeper.”
—John Ashbery (b. 1927)