Related papers: Comments on the height reducing property II

We present new techniques for removing arrows of bound quiver algebras, reducing thus the Finitistic Dimension Conjecture $\mathsf{(FDC)}$ for a given algebra to a smaller one. Unlike the classic arrow removal operation of…

Let $K$ be a field of characteristic zero. We deal with the algebraic closure of the field of fractions of the ring of formal power series $K[[x_1,\ldots,x_r]]$, $r\geq 2$. More precisely, we view the latter as a subfield of an iterated…

For a finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem consists in, given a graph $G$ and an integer $k$, decide whether there exists $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…

We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…

Let R be a two-dimensional regular local ring having an algebraically closed residue field and let a be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of a by means of the dual graph of the…

Let $f_{1}, \ldots, f_{k}$ be polynomials defining an algebraic set in affine $n$-space over a finite field. Suppose $k>n$. We prove that there exists a system of polynomials $g_{1}, \ldots, g_{n}$, each being a linear combination with…

It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra $A$ there exists a Hopf algebra $H$ containing $A$ as a Hopf subalgebra such that $H$ is not flat over $A$. On the other hand, there is a class of…

A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…

This note deals with some effective results in Mahler's method. In a recent work, we used a theorem of Philippon to show that given a Mahler function $f(z)$ in ${\bf k}\{z\}$, where ${\bf k}$ denotes a number field, and an algebraic number…

We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…

Recall that a triangular Hopf algebra A is said to have the Chevalley property if the tensor product of any two simple A-modules is semisimple, or, equivalently, if the radical of A is a Hopf ideal. There are two reasons to study this class…

Let $\Lambda$ be the limit set of an infinite conformal iterated function system and let $F$ denote the set of fixed points of the maps. We prove that the box dimension of $\Lambda$ exists if and only if \[ \overline{\dim}_{\mathrm B} F\leq…

We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…

Let $\Gamma$ be a finitely generated subgroup of the multiplicative group $\G_m^2(\bar{Q})$. Let $p(X,Y),q(X,Y)\in\bat{Q}$ be two coprime polynomials not both vanishing at $(0,0)$; let $\epsilon>0$. We prove that, for all $(u,v)\in\Gamma$…

An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…

Let $f(X)$ be a nonconstant polynomial over $\mathbb{F}_{q}$, with a nonzero constant term. The order of $f(X)$ is a classical notion in the theory of polynomials over finite fields, and recently the definition of freeness of binomials of…

Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…

We prove that if $P(X) \in \mathbb{Z}[X]$ is an integer polynomial of degree $n$ and having $P(0) = 1$, then either $P(X)$ is a product of cyclotomic polynomials, or else at least one of the complex roots of $P$ belongs to the disk $|z|…

We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…