Related papers: On equations over direct powers of algebraic struc…

After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.

We consider $n\times n$ real-valued matrices $A = (a_{ij})$ satisfying $a_{ii} \geq a_{i,i+1} \geq \dots \geq a_{in} \geq a_{i1} \geq \dots \geq a_{i,i-1}$ for $i = 1,\dots,n$. With such a matrix $A$ we associate a directed graph $G(A)$. We…

We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.

We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the results are applied to prove that certain Artinian complete…

We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…

We introduce the notion of biexactness for general von Neumann algebras, naturally extending the notion from group theory. We show that biexactness implies solidity for von Neumann algebras, and that many of the examples of solid von…

We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity.

We study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantized Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained in [arXiv:0906.2930] for down-up…

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder…

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] are derived in terms…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

We define a natural lattice structure on all subsets of a finite root system that extends the weak order on the elements of the corresponding Coxeter group. For crystallographic root systems, we show that the subposet of this lattice…

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…

We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…

We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…

Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite general linear group. In this paper, we study a common…

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…