Searcharxiv⌕ Search

arXiv subjects

Agnes Szendrei

Publications and source records attributed to Agnes Szendrei.

15 recordsLinked to original sources
arXiv2026

Locally finite Schreier Varieties

A variety $\mathcal{V}$ is called a Schreier variety if every subalgebra of a $\mathcal{V}$-free algebra is a $\mathcal{V}$-free algebra. We use ideas from Tame Congruence Theory to classify locally finite Schreier varieties. One version of the classification theorem states that a locally finite variety $\mathcal{V}$ is a Schreier variety if and only if (i) every finite algebra in $\mathcal{V}$ is a $\langle 0,1\rangle$-minimal algebra and (ii) if $\mathcal{V}$ has a constant $1$-ary term operation, then $\mathcal{V}$ also has a constant $0$-ary term operation.

math.RA↗
arXiv2022

Ultralocally Closed Clones

Given a clone C on a set A, we characterize the clone of operations on A which are local term operations of every ultrapower of the algebra $(A; C)$.

math.LO↗
arXiv2021

Algebras from Congruences

We present a functorial construction which, starting from a congruence $α$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences between 0 and $α$ on A, this isomorphism preserves higher commutators and TCT types, and C inherits all idempotent Maltsev conditions from A. As applications of this construction, we first show that supernilpotence is decidable for congruences of finite algebras in varieties that omit type 1. Secondly, we prove that the subpower membership problem for finite algebras with a cube term can be effectively reduced to membership questions in subdirect products of subdirectly irreducible algebras with central monoliths. As a consequence, we obtain a polynomial time algorithm for the subpower membership problem for finite algebras with a cube term in which the monolith of every subdirectly irreducible section has a supernilpotent centralizer.

math.LO↗
arXiv2020

Minimal abelian varieties of algebras, I

We show that any abelian variety that is not affine has a nontrivial strongly abelian subvariety. In later papers in this sequence we apply this result to the study of minimal abelian varieties.

math.LO↗
arXiv2020

Neutrabelian algebras

We introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.

math.RA↗
arXiv2019

Divisibility Theory of Commutative Rings and Ideal Distributivity

We begin by investigating the class of commutative unital rings in which no two distinct elements divide the same elements. We prove that this class forms a finitely axiomatizable, relatively ideal distributive quasivariety, and it equals the quasivariety generated by the class of integral domains with trivial unit group. We end the paper by proving a representation theorem that provides more evidence to the conjecture that Bézout monoids describe exactly the monoids of finitely generated ideals of commutative unital rings with distributive ideal lattice.

math.RA↗
arXiv2019

Random Models of Idempotent Linear Maltsev Conditions. I. Idemprimality

We extend a well-known theorem of Murski\vı to the probability space of finite models of a system $\mathcal{M}$ of identities of a strong idempotent linear Maltsev condition. We characterize the models of $\mathcal{M}$ in a way that can be easily turned into an algorithm for producing random finite models of $\mathcal{M}$, and we prove that under mild restrictions on $\mathcal{M}$, a random finite model of $\mathcal{M}$ is almost surely idemprimal. This implies that even if such an $\mathcal{M}$ is distinguishable from another idempotent linear Maltsev condition by a finite model $\mathbf{A}$ of $\mathcal{M}$, a random search for a finite model $\mathbf{A}$ of $\mathcal{M}$ with this property will almost surely fail.

math.LO↗
arXiv2016

Varieties whose finitely generated members are free

We prove that a variety of algebras whose finitely generated members are free must be definitionally equivalent to the variety of sets, the variety of pointed sets, a variety of vector spaces over a division ring, or a variety of affine vector spaces over a division ring.

math.RA↗
arXiv2016

Cube term blockers without finiteness

We show that an idempotent variety has a $d$-dimensional cube term if and only if its free algebra on two generators has no $d$-ary compatible cross. We employ Hall's Marriage Theorem to show that a variety of finite signature whose fundamental operations have arities $n_1, \ldots, n_k$ has a $d$-dimensional cube term if and only if it has one of dimension $d=1+\sum_{i=1}^k (n_i-1)$. This lower bound on dimension is shown to be sharp. We show that a pure cyclic term variety has a cube term if and only if it contains no $2$-element semilattice. We prove that the Maltsev condition "existence of a cube term" is join prime in the lattice of idempotent Maltsev conditions.

math.RA↗
arXiv2015

Dualizable algebras with parallelogram terms

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but more importantly proves that every finite module, group or ring in a residually small variety is dualizable.

math.RA↗
arXiv2014

Growth Rates of Algebras, II: Wiegold Dichotomy

We investigate the function $d_\mathbf{A}(n)$, which gives the size of a least size generating set for $\mathbf{A}^n$, in the case where $\mathbf{A}$ has a cube term. We show that if $\mathbf{A}$ has a $k$-cube term and $\mathbf{A}^k$ is finitely generated, then $d_\mathbf{A}(n) \in O(\log(n))$ if $\mathbf{A}$ is perfect and $d_\mathbf{A}(n) \in O(n)$ if $\mathbf{A}$ is imperfect. When $\mathbf{A}$ is finite, then one may replace "Big Oh" with "Big Theta" in these estimates.

math.RA↗
arXiv2009

The submaximal clones on the three-element set with finitely many relative R-classes

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.

math.RA↗
arXiv2007

Equivalence of operations with respect to discriminator clones

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In this paper we prove that if C is a discriminator clone on a finite set, then there are only finitely many C-equivalence classes. Moreover, we show that the smallest discriminator clone is minimal with respect to this finiteness property. For discriminator clones of Boolean functions we explicitly describe the associated equivalence relations.

math.RA↗