4 papers
Divide and Transfer: Non-Unique Factorizations Beyond Commutativity
Daniel Smertnig
Unique factorization fails in many rings and monoids, but divisor and transfer homomorphisms provide tools to understand non-unique factorizations. In this expository article, we f…
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…
Factoring through monomial representations: arithmetic characterizations and ambiguity of weighted automata
Antoni Puch, Daniel Smertnig
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic prop…
A monoid-theoretical approach to infinite direct-sum decompositions of modules
Zahra Nazemian, Daniel Smertnig
Let be a class of modules over a ring , closed under direct sums over index sets of cardinality and isomorphisms, and such that the isomorphism classes form a s…