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?

Peter