1 | initial version |
In a field there are no nonzero non-invertible elements.
Being "unique factorisation" or "euclidean" depends on properties of such elements.
Better ask such questions about the ring of integers of that field:
sage: OK = K.ring_of_integers()
sage: OK in UniqueFactorizationDomains
False
sage: OK in EuclideanDomains
False