8 citations · 19 across the 18 of their papers we have counts for
24 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…
What is the weakest idempotent Maltsev condition that implies that abelian tolerances generate abelian congruences?
Keith A. Kearnes, Emil W. Kiss
We answer the question in the title. In the process, we correct an error in our AMS Memoir The Shape of Congruence Lattices.
Relative Maltsev Definability of some Commutator Properties
Keith A. Kearnes
We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.
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…
A note on "A minimal congruence lattice representation for ''
Keith A. Kearnes
We reprove a theorem of Bunn, Grow, Insall, and Thiem, which asserts that a minimal congruence lattice representation for has size , and is an expansion of a…
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.
Representing subalgebras as retracts of finite subdirect powers
Keith A. Kearnes, Alexander Rasstrigin
We prove that if is an algebra that is supernilpotent with respect to the -term higher commutator, and is a subalgebra of , then i…
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…
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.''
An uncountable Jónsson algebra in a minimal variety
Jordan DuBeau, Keith A. Kearnes
We construct a Jónsson algebra of cardinality in the variety of Jónsson-Tarski algebras.
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,…
Solvable quotients of subdirect products of perfect groups are nilpotent
Keith Kearnes, Peter Mayr, Nik Ruškuc
We prove the statement in the title and exhibit examples of quotients of arbitrary nilpotency class. This answers a question by D. F. Holt.
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…
Relatively congruence modular quasivarieties of modules
Keith A. Kearnes
We show that the quasiequational theory of a relatively congruence modular quasivariety of left -modules is determined by a two-sided ideal in together with a filter of left…
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.
Modularity prevents tails
Keith A. Kearnes, Emil W. Kiss
We establish a direct correspondence between two congruence poroperties for finite algebras. The first property is that minimal sets of type i omit tails. The second property is th…
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…
Projectivity and isomorphisms of strictly simple algebras
Keith A. Kearnes, Ågnes Szendrei
We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads…
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…