73 citations · 300 across the 27 of their papers we have counts for
6 papers · 1 filter
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…
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…
Lattices over Bass rings and graph agglomerations
Nicholas R. Baeth, Daniel Smertnig
We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring through the factorization theory of the corresponding monoid $T(R)…
Factoriality and class groups of cluster algebras
Ana Garcia Elsener, Philipp Lampe, Daniel Smertnig
Locally acyclic cluster algebras are Krull domains. Hence their factorization theory is determined by their (divisor) class group and the set of classes containing height-1 prime i…
A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems
Nicholas R. Baeth, Alfred Geroldinger, David J. Grynkiewicz +1
Let be a ring and let be a small class of right -modules which is closed under finite direct sums, direct summands, and isomorphisms. Let $\mathcal V (\mathcal…
Factorization in the self-idealization of a PID
Gyu Whan Chang, Daniel Smertnig
Let be a principal ideal domain and be its self-idealization. It is known that is a commutative no…