相关论文: On equations over direct powers of algebraic struc…

This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the…

A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.

The aim of this note is to give an effective criterion to verify whether a cubic polynomial over a non-Archimedean field has a weak N\'{e}ron model or not.

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of…

We study the problem of existence of pushouts in the category of algebraic sets over an infinite field. This problem can be reduced to asking whether the property of being a finitely generated algebra over a field, or a Noetherian ring in…

Let K be a field of characteristic zero. Motivated by the conjecture that an enveloping algebra U(g) is Noetherian only if g is finite dimensional, we define the notion of weakly Noetherian Lie algebras. The main result, Theorem A, states…

We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…

In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence…

We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…

In this short paper, we establish the local Noetherian property for the linear categories of Brauer, partition algebras, and other related categories of diagram algebras with no restrictions on their various parameters.

The aim of this paper is to compare and contrast the class of residually finite groups with the class of equationally Noetherian groups - groups over which every system of coefficient-free equations is equivalent to a finite subsystem. It…

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…

We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the…

A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals…

This paper studies systems of polynomial equations that provide information about orientability of matroids. First, we study systems of linear equations over GF(2), originally alluded to by Bland and Jensen in their seminal paper on weak…

We show that the values of a certain family of weakly holomorphic modular functions at points in the divisors of any meromorphic modular form with algebraic Fourier coefficients are algebraic. We use this to extend the classical result of…

We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an…

In this paper we extend the almost complex Poisson structures from almost complex manifolds to almost complex Lie algebroids. Examples of such structures are also given and the almost complex Poisson morphisms of almost complex Lie…

We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…