Related papers: Finitely generated equational classes
We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…
We study the class of finite lattices that are isomorphic to the congruence lattices of algebras from a given finitely generated congruence-distributive variety. If this class is as large as allowed by an obvious necessary condition, the…
We denote by Conc(A) the semilattice of all finitely generated congruences of an (universal) algebra A, and we define Conc(V) as the class of all isomorphic copies of all Conc(A), for A in V, for any variety V of algebras. Let V and W be…
We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
A finitely generated group $G$ is said to be condensed if its isomorphism class in the space of finitely generated marked groups has no isolated points. We prove that every product variety $\mathcal{UV}$, where $\mathcal{U}$ (respectively,…
It is proved that for any natural number $n$ the subalgebra of a free finitely generated alternative algebra generated by all the words on generators whose length is a multiple of $n$ (the Veronese $n$-subalgebra), is finitely generated.
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
In tropical geometry, there are several important classes of ideals and congruences such as tropical ideals, bend congruences, and the congruences of the form $\mathbf E(Z)$. Although they are analogues of the concept of ideals of rings, it…
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…
In an earlier work, the author observed that Boolean inverse semi-groups, with semigroup homomorphisms preserving finite orthogonal joins, form a congruence-permutable variety of algebras, called biases. We give a full description of…
The article aims at describing all covers of any finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (concerning their order). Also, all subdirectly irreducible members of…
If V is a finitely generated variety such that the first-order theory of the finite members of V is decidable, we show that V is residually finite, and in fact has a finite bound on the sizes of subdirectly irreducible algebras. This result…
Profinite algebras are exactly those that are isomorphic to inverse limits of finite algebras. Such algebras are naturally equipped with Boolean topologies. A variety $\mathcal V$ is standard if every Boolean topological algebra with the…
A variety is a class of algebraic structures axiomatized by a set of equations. An equation is linear if there is at most one occurrence of an operation symbol on each side. We show that a variety axiomatized by linear equations has the…
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers. We construct such a homeomorphism by choosing a small…