{"id":"palomar/PALOMAR-2026-08-28-000002","url":"https://github.com/Arthur742Ramos/NagataFactoriality/tree/9ebcfa77a4f7eab6fdb663e7f151ceeb48abdff7","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-28-000002-v1.json","repo":"https://github.com/Arthur742Ramos/NagataFactoriality","tags":["math.AC","cs.LO","msc:13A05","msc:13B30","msc:03B35","commutative-algebra","lean","factoriality","unique-factorization"],"score":0,"title":"Arthur742Ramos/NagataFactoriality","trust":"high","domain":"math.AC","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy J. G. B. de Queiroz"],"reviews":0,"subject":"math.AC","summary":"A Lean 4 and Mathlib formalization of Nagata's factoriality theorem for noetherian integral domains. It proves that unique factorization descends from a localization when every denominator is a finite product of prime elements, packages the specialization to submonoids generated by sets of primes, and demonstrates the method with a Nagata-based polynomial UFD theorem.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-28","reactions":{},"formalized":true}