21 citations · 50 across the 15 of their papers we have counts for
22 papers
Locally finite Schreier Varieties
Keith A. Kearnes, Andrew Moorhead, Agnes Szendrei
A variety is called a Schreier variety if every subalgebra of a -free algebra is a -free algebra. We use ideas from Tame Congruence Theory t…
Ivo G. Rosenberg's Work on Maximal Clones and Minimal Clones
Agnes Szendrei
The aim of this paper is to honor Ivo G. Rosenberg by describing some of his most influential results and their impact in logic, discrete mathematics, algebra, and computer science…
Characterizing the commutator in varieties with a difference term
Keith A. Kearnes, Ágnes Szendrei, Ross Willard
We extend the validity of Kiss's characterization of the commutator from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in o…
Neutrabelian algebras
Keith A. Kearnes, Connor Meredith, Agnes Szendrei
We introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.
Ultralocally Closed Clones
Keith A. Kearnes, Agnes Szendrei
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 .
Minimal abelian varieties of algebras, I
Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei
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 abel…
Algebras from Congruences
Peter Mayr, Agnes Szendrei
We present a functorial construction which, starting from a congruence of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lat…
Is supernilpotence super nilpotence?
Keith A. Kearnes, Ágnes Szendrei
We show that the answer to the question in the title is: ``Yes, for finite algebras.''
Random Models of Idempotent Linear Maltsev Conditions. I. Idemprimality
Clifford Bergman, Agnes Szendrei
We extend a well-known theorem of Murski\vı to the probability space of finite models of a system of identities of a strong idempotent linear Maltsev condition. We ch…
Divisibility Theory of Commutative Rings and Ideal Distributivity
P. N. Anh, Keith A. Kearnes, Agnes Szendrei
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,…
The Subpower Membership Problem for Finite Algebras with Cube Terms
Andrei Bulatov, Peter Mayr, Ágnes Szendrei
The subalgebra membership problem is the problem of deciding if a given element belongs to an algebra given by a set of generators. This is one of the best established computationa…
Cube term blockers without finiteness
Keith A. Kearnes, Agnes Szendrei
We show that an idempotent variety has a -dimensional cube term if and only if its free algebra on two generators has no -ary compatible cross. We employ Hall's Marriage Theo…
Varieties whose finitely generated members are free
Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei
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 ve…
Dualizable algebras with parallelogram terms
Keith A. Kearnes, Agnes Szendrei
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 dualizab…
Growth rates of algebras, I: pointed cube terms
Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei
We investigate the function d_A(n), which gives the size of a least size generating set for A^n.
Growth Rates of Algebras, II: Wiegold Dichotomy
Keith A. Kearnes, Emil W. Kiss, Agnes Szendrei
We investigate the function , which gives the size of a least size generating set for , in the case where has a cube term. We show that…
Growth Rates of Algebras, III: Growth Rates of Solvable Algebras
Keith A. Kearnes, Emil W. Kiss, Ágnes Szendrei
We investigate how the behavior of the function d_A(n) that gives the size of a least size generating set for A^n, influences the structure of a finite solvable algebra A.
The submaximal clones on the three-element set with finitely many relative R-classes
Erkko Lehtonen, Agnes Szendrei
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…
Clones with finitely many relative R-classes
Erkko Lehtonen, Ágnes Szendrei
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 iff each one is a substitution instance o…
Equivalence of operations with respect to discriminator clones
Erkko Lehtonen, Agnes Szendrei
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 sub…
Self-rectangulating varieties of type 5
Keith A. Kearnes, Ågnes Szendrei
We show that a locally finite variety which omits abelian types is self-regulating if and only if it has a compatible semilattice term operation. Such varieties must have a type-se…
The relationship between two commutators
Keith A. Kearnes, Ågnes Szendrei
We clarify the relationship between the linear commutator and the ordinary commutator by showing that in any variety satisfying a nontrivial idempotent Mal'cev condition the linear…