Generalizations of Samuel's criteria for a ring to be a unique factorization domain

Abstract

We give several criteria for a ring to be a UFD, including generalizations of some criteria due to P. Samuel. These criteria are applied to construct, for any field k, (1) a Z-graded non-noetherian rational UFD of dimension 3 over k, and (2) k-affine rational UFDs defined by trinomial relations.