Related papers: Noetherian criteria for dimer algebras

Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is…

We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Let $\mathcal{P}$ be the class of rings for which every indecomposable right module is pure-projective or pure-injective. When $R$ is a Noetherian local commutative ring of maximal ideal $P$, it is proven that $R\in\mathcal{P}$ if and only…

We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\mathfrak A$ satisfies…

We prove a mixed-characteristic analogue of Kunz's theorem in terms of perfectoid towers: a Noetherian local ring of residue characteristic $p$ is regular if and only if it admits a flat map to a Noetherian ring that extends to a perfectoid…

This paper develops the homological backbone of the theory of non-commutative $n$-ary $\Gamma$-semirings. Starting from an $n$-ary $\Gamma$-semiring $(T,+,\tilde{\mu})$ and its $\Gamma$-ideals, we work in the slot-sensitive categories of…

It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish…

The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph $G$ is said to be $n$-rotation symmetric if the cyclic group of order $n$ is a subgroup of the…

This paper establishes a necessary and sufficient condition for the coincidence of non-commutative $\log$-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of…

In this paper it is shown that every irreducible vertex algebra of countable dimension and every simple vertex operator algebra are nondegenerate in the sense of Etingof and Kazhdan.

Let $A$ be a Noetherian ring and let $I$ be an ideal in $A$. Let $\mathcal{F} = \{ J_n \}_{n \geq 0}$ be a multiplicative filtration of ideals in $A$ such that $\mathcal{R}(\mathcal{F}) = \bigoplus_{n \geq 0} J_n$ is a finitely generated…

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $\Lambda$, we study the set…

We establish a characterization of dualizing modules among semidualizing modules. Let R be a finite dimensional commutative Noetherian ring with identity and C a semidualizing R-module. We show that C is a dualizing R-module if and only if…

Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…

We prove that the group algebra $KG$ of a group $G$ over a field $K$ is primitive, provided that $G$ has a free subgroup with the same cardinality as $G$, and that $G$ satisfies the following condition $(\ast)$: for each subset $M$ of $G$…

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…

Let A be a commutative ring, and let \a be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically \a-torsion complexes. We prove…

We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A. Polishchuk. Our aim is to understand how these rings give rise to an arithmetic structure on the noncommutative torus. We start by giving…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…