73 citations · 300 across the 27 of their papers we have counts for
28 papers
Mahler series with multiplicative coefficient sequences
Jason Bell, Daniel Smertnig
We prove that every Mahler series, over a field of characteristic , with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit…
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…
Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata
Filip Mazowiecki, Antoni Puch, Daniel Smertnig
In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are intere…
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…
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…
Monoid algebras and graph products
Wilfried Imrich, Igor Klep, Daniel Smertnig
In this note, we extend results about unique roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product…
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…
Duality of Lattices Associated to Left and Right Quotients
Jason Bell, Daniel Smertnig, Hellis Tamm
We associate lattices to the sets of unions and intersections of left and right quotients of a regular language. For both unions and intersections, we show that the lattices we pro…
Computing the linear hull: Deciding Deterministic? and Unambiguous? for weighted automata over fields
Jason P. Bell, Daniel Smertnig
The (left) linear hull of a weighted automaton over a field is a topological invariant. If the automaton is minimal, the linear hull can be used to determine whether or not the aut…
On noncommutative bounded factorization domains and prime rings
Jason P. Bell, Ken Brown, Zahra Nazemian +1
A ring has bounded factorizations if every cancellative nonunit can be written as a product of atoms and there is a bound on the lengths of such factorizations. Th…
-finite multivariate series with arithmetic restrictions on their coefficients
Jason Bell, Daniel Smertnig
A multivariate, formal power series over a field is a Bézivin series if all of its coefficients can be expressed as a sum of at most elements from a finitely generated subg…
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)…
A height gap theorem for coefficients of Mahler functions
Boris Adamczewski, Jason Bell, Daniel Smertnig
We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five differe…
Noncommutative rational Pólya series
Jason Bell, Daniel Smertnig
A (noncommutative) Pólya series over a field is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of . We show that rati…
Definite orders with locally free cancellation
Daniel Smertnig, John Voight
We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modul…
On basic and Bass quaternion orders
Sara Chari, Daniel Smertnig, John Voight
A quaternion order O over a Dedekind domain R is Bass if every R-superorder is Gorenstein, and O is basic if it contains an integrally closed quadratic R-order. In this article, we…
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…
Arithmetical invariants of local quaternion orders
Nicholas R. Baeth, Daniel Smertnig
Let be a DVR, let be its quotient field, and let be a -order in a quaternion algebra over . The elasticity of is $ρ(R^\bullet) = \sup\{\, k/l : u_…
Factorizations in bounded hereditary Noetherian prime rings
Daniel Smertnig
If is a monoid and with atoms (irreducible elements) , then is a length of , the set of lengths of is denoted by $\mathsf…
Factorizations of Elements in Noncommutative Rings: A Survey
Daniel Smertnig
We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative…
Every abelian group is the class group of a simple Dedekind domain
Daniel Smertnig
A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, t…
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 theory: From commutative to noncommutative settings
Nicholas R. Baeth, Daniel Smertnig
We study the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in noncommutative rings. To do so, we extend concepts from the commutative theory of no…