Related papers: Adapted algebras for the Berenstein-Zelevinsky con…

In this note, we prove that the generalized Auslander-Reiten conjecture is preserved under derived equivalences between Artin algebras.

We prove that each semialgebraic subset of $\R^n$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving…

In this article, we prove the $p$-adic Kazhdan-Lusztig hypothesis for $\mathrm{GL}_n(F)$. While the approach via graded affine Hecke algebras due to recent work of Solleveld leads to more general results, this article serves to completes…

Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric theory of continued fractions, we give a sufficient…

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example of a non-Banach Frechet algebra with two inequivalent…

We provide a reduction in the classification problem for non-compact, homogeneous, Einstein manifolds. Using this work, we verify the (Generalized) Alekseevskii Conjecture for a large class of homogeneous spaces.

Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K. Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a correspondence between finite dimensional symmetric algebras and homogeneous tuples of…

By using nonstandard analysis, we prove embeddability properties of difference sets $A-B$ of sets of integers. (A set $A$ is "embeddable" into $B$ if every finite configuration of $A$ has shifted copies in $B$.) As corollaries of our main…

From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie n-algebras. We also consider the…

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…

The present paper is devoted to provide conditions for the Levi--Malcev theorem to hold or not to hold (i.e. for two Levi subalgebras to be or not conjugate by an inner automorphism) in the context of finite-dimensional Leibniz algebras…

Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our…

We consider from a geometric point of view the conjectural fundamental lemma of Langlands and Shelstad for unitary groups over a local field of positive characteristic. We introduce projective algebraic varieties over the finite residue…

We show that the finitistic dimension conjecture holds for all finite dimensional algebras if and only if, for all finite dimensional algebras, the finitistic dimension of an algebra being finite implies that the finitistic dimension of its…

We show that the Jacobian conjecture of the two dimensional case is true.

In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…