Related papers: On irreducible algebraic sets over linearly ordere…
We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.
We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…
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 investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We study the algebraic exceptional set for surfaces (S,B) of log general type, when B has at least three irreducible components; we prove that in most cases it is finite or empty.
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras…
We give improved lower bounds for the number of solutions of some $S$-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method…
In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irreducible solutions from which we can build all the…
We investigate sets of the common zeros of non-constant semi-invariants for regular modules over canonical algebras. In particular, we show that if the considered algebra is tame then for big enough vectors these sets are complete…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
In this paper, we study equations over Brandt semigroup $B_n$. We compute that the number of unsolvable equations in one variable asymptotically equals $\frac{2}{n^2}$, and the average number of solutions of these equations asymptotically…