## 8 Citations

The valuation pairing on an upper cluster algebra

- Mathematics
- 2022

. It is known that many (upper) cluster algebras are not unique fac- torization domains. We exhibit the local factorization properties with respect to any given seed t : any non-zero element in a…

A geometric q ‐character formula for snake modules

- MathematicsJournal of the London Mathematical Society
- 2020

Let C be the category of finite‐dimensional modules over the quantum affine algebra Uq(ĝ) of a simple complex Lie algebra g . Let C− be the subcategory introduced by Hernandez and Leclerc. We prove…

On the distribution of prime divisors in class groups of affine monoid algebras

- MathematicsCommunications in Algebra
- 2022

Abstract We investigate the class groups and the distribution of prime divisors in affine monoid algebras over fields and thereby extend the result of Kainrath that every finitely generated integral…

Uniform Symbolic Topologies in Non-Regular Rings

- Mathematics
- 2019

When does a Noetherian commutative ring R have uniform symbolic topologies (USTP) on primes – read, when does there exist an integer D > 0 such that the symbolic power P (Dr) ⊆ P r for all prime…

Sets of arithmetical invariants in transfer Krull monoids

- MathematicsJournal of Pure and Applied Algebra
- 2019

On transfer homomorphisms of Krull monoids

- MathematicsBollettino della Unione matematica italiana
- 2021

This paper strengthens and refine the transfer homomorphism onto a monoid of zero-sum sequences over a subset of its class group for Krull monoids with finitely generated class group.

A characterization of length-factorial Krull monoids

- Mathematics
- 2021

An atomic monoid is length-factorial if each two distinct factorizations of any element have distinct factorization lengths. We provide a characterization of length-factorial Krull monoids in terms…

A realization result for systems of sets of lengths

- MathematicsIsrael Journal of Mathematics
- 2021

Let $\mathcal L^*$ be a family of finite subsets of $\mathbb N_0$ having the following properties.
(a). $\{0\}, \{1\} \in \mathcal L^*$ and all other sets of $\mathcal L^*$ lie in $\mathbb N_{\ge…

## References

SHOWING 1-10 OF 48 REFERENCES

Acyclic cluster algebras from a ring theoretic point of view

- Mathematics
- 2012

The article gives a ring theoretic perspective on cluster algebras. Gei{\ss}-Leclerc-Schr\"oer prove that all cluster variables in a cluster algebra are irreducible elements. Furthermore, they…

Cluster algebras III: Upper bounds and double Bruhat cells

- Mathematics
- 2003

We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of…

Cluster algebras II: Finite type classification

- Mathematics
- 2002

This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many…

Factorial cluster algebras

- Mathematics
- 2011

We show that cluster algebras do not contain non-trivial units and that all cluster variables are irreducible elements. Both statements follow from Fomin and Zelevinsky's Laurent phenomenon. As an…

Cluster algebra structures on Poisson nilpotent algebras

- Mathematics
- 2018

Various coordinate rings of varieties appearing in the theory of Poisson Lie groups and Poisson homogeneous spaces belong to the large, axiomatically defined class of symmetric Poisson nilpotent…

Cluster algebras IV: Coefficients

- MathematicsCompositio Mathematica
- 2007

We study the dependence of a cluster algebra on the choice of coefficients. We write general formulas expressing the cluster variables in any cluster algebra in terms of the initial data; these…

From triangulated categories to cluster algebras

- Mathematics
- 2005

The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra $\mathcal{A}$ of finite type can be realized as a…

Quantum Cluster Algebra Structures on Quantum Nilpotent Algebras

- Mathematics
- 2017

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that…