gcd oops

Michael Ackerman ack@nethere.com
Tue, 18 Dec 2001 16:26:46 -0800

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.

Michael Ackerman