gcd oops

Sorry for an error in my previous message. The definition there of a gcd works only in a prinicpal ideal domain (which covers all the rings mentioned in the examples). According to Bourbaki, chapter on ordered groups, the gcd of two non-zero elements of a UFD A is well-defined as an element of (A-{0})/units, a quotient monoid. So in this context gcd(0, _) is undefined. But Bourbaki adds that this concept is `sometimes' extended to the gcd of a finite family (x_i) of elements some of which may be zero by taking the gcd to be an element d such that for all z, z divides d iff z divides each x_i. Cheers, Michael Ackerman