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math.AC2026
Factoriality and Class Groups of Upper Cluster Algebras and Finite Laurent Intersection Rings: A Computational Approach
Mara Pompili, Daniel Smertnig
We study factoriality and the class groups of locally acyclic cluster algebras. To do so, we introduce a new class of rings called finite Laurent intersection rings (FLIRs), which…
math.AC2025
Primes and absolutely or non-absolutely irreducible elements in atomic domains
Victor Fadinger, Sophie Frisch, Sarah Nakato +2
We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes…