I am reading Dummit and Foote Ch 8 - Euclidean, Prinipal Ideal and Unique Factorization Domains.
On page 274 D&F write: (see attached)
"Thus a greatest common divisor (if such exists) ... ..."
Even when two elements of a ring are prime a gcd exists ... ???
Can anyone give me examples of cases where a gcd does not exist for two elements of a ring?