3 papers
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
On transfer homomorphisms in commutative rings with zero-divisors
Aqsa Bashir, Mara Pompili
We study the arithmetic of monoids of regular elements of commutative rings with zero-divisors. Our focus is on Krull rings and on some of their generalizations (such as weakly Kru…
math.AC2025
Every finitely generated abelian group is the class group of a generalized cluster algebra
Mara Pompili
We determine the class group of those generalized cluster algebras that are Krull domains. In particular, this provides a criterion for determining whether or not a generalized clu…