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arXiv · 2102.06642

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

Daniel Daigle·Gene Freudenburg·Takanori Nagamine
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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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Daniel Daigle, Gene Freudenburg, Takanori Nagamine. 2021-02-12. Generalizations of Samuel's criteria for a ring to be a unique factorization domain. https://arxiv.org/abs/2102.06642

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