Generalizations of Samuel's criteria for a ring to be a unique factorization domain
Daniel Daigle, Gene Freudenburg, Takanori Nagamine
TL;DR
This paper extends Samuel's criteria to identify when a ring is a UFD, and constructs specific examples of non-noetherian and trinomial-defined UFDs over any field.
Contribution
It generalizes Samuel's criteria for UFDs and constructs new classes of UFDs with particular properties over arbitrary fields.
Findings
Constructed a Z-graded non-noetherian rational UFD of dimension three over any field
Developed k-affine rational UFDs defined by trinomial relations
Extended criteria for UFDs to broader classes of rings
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 three over k, and (2) k-affine rational UFDs defined by trinomial relations.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Commutative Algebra and Its Applications