相关论文: Infinite irredundant equational axiomatisability f…

The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…

We give an elementary proof of a result which is not as well known as it should be: a ring with a specified finite number of zero divisors is finite, with a precise bound on its order.

We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…

Divisibility monoids are a natural lattice-theoretical generalization of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the involved divisibility lattices is kept as an hypothesis, but the relations between the…

We provide an alternative proof that the finite rational linear combination of radicals, under certain constraint, are linearly independent over $\mathbb{Q}$.

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…

We show the irredundancy, necessity and sufficiency of inequalities corresponding to intersections whose ``Witten Bundle'' is polyrigid for the product of unitary matrices problem.

A finitely generated solvable group with unbounded iterated identity is constructed.

We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.

A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a…

We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element…

It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary…

We characterize those complete commutative positive linear ordered monoids $W$ such that whenever $f$ is a map from a Cauchy complete $W$-metric space to itself, the existence of a fixed point of $f$ is independent of the background model…

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…

We prove that any finite, abstract n-polytope is covered by a finite, abstract regular n-polytope.

The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.

We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

In this paper we show that the membership problems for finitely generated submonoids and for rational subsets are recursively equivalent for groups with two or more ends.