Related papers: Infinite irredundant equational axiomatisability f…

We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

We give axiomatic foundations for non-finitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a problem of Rado of 1966.

We present a general method for proving that a semigroup is non-finitely based. The method is strong enough to cover the non-finite basis arguments in articles [1,3,4,5,7,8, 11,14,16,21,27,31,36,37]. In particular, the method allows to…

We exhibit an example of a finitely presented monoid that is congruence-free and simple but not bisimple.

Up to isomorphism, there exist two non-isomorphic two-element monoids. We show that the identities of the free product of every pair of such monoids admit no finite basis.

In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.

A $\lambda$-quiddity of size $n$ is an $n$-tuple of elements from a fixed set, which is a solution to a matrix equation that arises in the study of Coxeter's friezes. The study of these solutions involves in particular the use of a notion…

We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank of the group. We give examples to show that this type of…

The class of all subdirectly irreducible groups belonging to a variety generated by a finite nilpotent group can be axiomatised by a finite set of elementary sentences.

Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…

Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…

We give a new proof that free Burnside groups of sufficiently large even exponents are infinite. The method is very flexible and can also be used to study (partially) periodic quotients of any group which admits an action on a hyperbolic…

We introduce the theory of monoidal Groebner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Groebner bases of ideals that are stable under the action of a monoid. The main…

It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a…

We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of…

We show that the monoid of all injective and extensive partial transformations of a chain with three elements admits no finite basis of its identities. This completes solving of the finite basis problem for the monoids in the basic frame of…

We generalise the construction of infinite matroids from trees of matroids to allow the matroids at the nodes, as well as the field over which they are represented, to be infinite.