research overview
- Dr. Kearnes' research interests include the classification of equational theories, structure theory for finite algebras, and applications of combinatorics and model theory to algebra.
- Contact Info
Kearnes, Keith A
Positions
- Professor, Mathematics
Research Areas
Research
keywords
- associative algebras, commutative ring theory, finite group theory, universal algebra, lattice theory, model theory, combinatorics
Publications
selected publications
-
chapter
-
Relatively congruence modular quasivarieties of modules.
Outstanding Contributions to Logic.
221-232.
2018
- Left and right nilpotence degree are independent. 189-198. 2001
- Idempotent simple algebras. 529-572. 1996
- Congruence lattices of congruence semidistributive algebras. 63-78. 1995
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Relatively congruence modular quasivarieties of modules.
Outstanding Contributions to Logic.
221-232.
2018
-
conference proceeding
- Logic Colloquium 2004. xii+220-xii+220. 2008
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journal article
- Ultralocally Closed Clones. Journal of Multiple-Valued Logic and Soft Computing. 509-538. 2025
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Relative Maltsev definability of some commutator properties.
International Journal of Algebra and Computation.
391-433.
2023
-
Correction to “A finite basis theorem for difference-term varieties with a finite residual bound”.
Transactions of the American Mathematical Society - Series B.
343-344.
2022
-
Characterizing the commutator in varieties with a difference term.
Algebra Universalis.
2022
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Every minimal dual discriminator variety is minimal as a quasivariety.
Algebra Universalis.
2021
-
Minimal abelian varieties of algebras, I.
International Journal of Algebra and Computation.
205-217.
2021
-
Neutrabelian algebras.
Algebra Universalis.
2021
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Representing subalgebras as retracts of finite subdirect powers.
Algebra Universalis.
2020
-
AN UNCOUNTABLE JONSSON ALGEBRA IN A MINIMAL VARIETY.
Proceedings of the American Mathematical Society.
1765-1775.
2020
-
Is supernilpotence super nilpotence?.
Algebra Universalis.
2020
-
Commutative Rings Whose Principal Ideals Have Unique Generators.
Springer Proceedings in Mathematics and Statistics.
1-9.
2020
-
Solvable quotients of subdirect products of perfect groups are nilpotent.
Bulletin of the London Mathematical Society.
1016-1026.
2018
-
EXTENDING UFDS TO PIDS WITHOUT ADDING UNITS.
Journal of Commutative Algebra.
347-358.
2018
-
Varieties whose finitely generated members are free.
Algebra Universalis.
2018
- Subsets Closed Under a Family of Functions. American Mathematical Monthly. 756-756. 2018
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Cube term blockers without finiteness.
Algebra Universalis.
437-459.
2017
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Simpler Maltsev conditions for (weak) difference terms in locally finite varieties.
Algebra Universalis.
555-561.
2017
- The Number of Sylow Subgroups. American Mathematical Monthly. 471-472. 2017
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Dualizable algebras with parallelogram terms.
Algebra Universalis.
497-539.
2016
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Growth rates of algebras, III: finite solvable algebras.
Algebra Universalis.
199-222.
2016
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GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS.
Journal of the Australian Mathematical Society.
56-94.
2016
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A FINITE BASIS THEOREM FOR DIFFERENCE-TERM VARIETIES WITH A FINITE RESIDUAL BOUND.
Transactions of the American Mathematical Society.
2115-2143.
2016
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Growth rates of algebras, II: Wiegold dichotomy.
International Journal of Algebra and Computation.
555-566.
2015
-
Optimal strong Mal'cev conditions for omitting type 1 in locally finite varieties.
Algebra Universalis.
91-100.
2014
-
POLYNOMIAL EQUIVALENCE OF FINITE RINGS.
Journal of the Australian Mathematical Society.
244-257.
2014
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Jonsson posets and unary Jonsson algebras.
Algebra Universalis.
101-112.
2013
- The Shape of Congruence Lattices. Memoirs of the American Mathematical Society. 1-+. 2013
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Commuting Polynomial Operations of Distributive Lattices.
Order.
245-269.
2012
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The 3rd International Conference on Boolean Algebra, Lattice Theory, Universal Algebra, Set Theory and Set-theoretical Topology-BLAST 2010.
Order.
229-230.
2012
-
An easy test for congruence modularity.
Algebra Universalis.
375-392.
2012
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CLONES OF ALGEBRAS WITH PARALLELOGRAM TERMS.
International Journal of Algebra and Computation.
2012
-
The shape of congruence lattices.
Memoirs of the American Mathematical Society.
1-1.
2012
-
An axiomatic formation that is not a variety.
Journal of Group Theory.
233-241.
2010
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CARDINALITIES OF RESIDUE FIELDS OF NOETHERIAN INTEGRAL DOMAINS.
Communications in Algebra.
3580-3588.
2010
-
RESIDUALLY FINITE VARIETIES OF NONASSOCIATIVE ALGEBRAS.
Communications in Algebra.
3705-3727.
2010
-
On the functional completeness of simple tournaments.
Algebra Universalis.
475-478.
2009
-
Definable principal congruences and solvability.
Annals of Pure and Applied Logic.
30-49.
2009
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Axiomatizable and nonaxiomatizable congruence prevarieties.
Algebra Universalis.
323-335.
2008
-
Clones of 2-step nilpotent groups.
Algebra Universalis.
491-512.
2008
-
Clones closed under conjugation I: Clones with constants.
International Journal of Algebra and Computation.
7-58.
2008
-
Automorphism groups of squares and of free algebras.
International Journal of Algebra and Computation.
461-505.
2007
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p(n)-sequences of algebras with one fundamental operation.
Algebra Universalis.
69-75.
2007
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Quasivarieties of Modules Over Path Algebras of Quivers.
Studia Logica.
333-349.
2006
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Congruence lattices of locally finite algebras.
Algebra Universalis.
237-248.
2005
-
Clones of finite groups.
Algebra Universalis.
23-52.
2005
-
The triangular principle is equivalent to the triangular scheme.
Algebra Universalis.
373-383.
2005
-
Groups with identical subgroup lattices in all powers.
Journal of Group Theory.
385-402.
2004
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Minimal sets in finite rings.
Algebra Universalis.
81-109.
2004
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Residual smallness and weak centrality.
International Journal of Algebra and Computation.
35-59.
2003
-
Chief factor sizes in finitely generated varieties.
Canadian Journal of Mathematics.
736-756.
2002
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Hausdorff properties of topological algebras.
Algebra Universalis.
343-366.
2002
-
Generating singular transformations.
Semigroup Forum.
441-448.
2001
-
Collapsing permutation groups.
Algebra Universalis.
35-51.
2001
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Congruence join semidistributivity is equivalent to a congruence identity.
Algebra Universalis.
373-387.
2001
-
The join of two minimal clones and the meet of two maximal clones.
Algebra Universalis.
161-178.
2001
-
Categorical quasivarieties via Morita equivalence.
Journal of Symbolic Logic (JSL).
839-856.
2000
-
Almost all minimal idempotent varieties are congruence modular.
Algebra Universalis.
39-45.
2000
-
Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound.
Proceedings of the American Mathematical Society.
2841-2850.
1999
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Finite algebras of finite complexity.
Discrete Mathematics.
89-135.
1999
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A geometric consequence of residual smallness.
Annals of Pure and Applied Logic.
137-169.
1999
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A modification of Polin's variety.
Algebra Universalis.
229-231.
1999
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Finiteness properties of locally finite abelian varieties.
International Journal of Algebra and Computation.
157-168.
1999
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A characterization of locally finite varieties that satisfy a nontrivial congruence identity.
Algebra Universalis.
195-204.
1999
-
Congruence modular varieties with small free spectra.
Algebra Universalis.
165-181.
1999
-
Modularity prevents tails.
Proceedings of the American Mathematical Society.
11-19.
1999
- Subdirectly irreducible modes. Discussiones Mathematicae Algebra and Stochastic Methods. 129-145. 1999
- The classification of commutative minimal clones. Discussiones Mathematicae Algebra and Stochastic Methods. 147-178. 1999
-
The residual character of varieties generated by strictly simple term minimal algebras.
Algebra Universalis.
269-288.
1999
-
The relationship between two commutators.
International Journal of Algebra and Computation.
497-531.
1998
-
Minimal sets and varieties.
Transactions of the American Mathematical Society.
1-41.
1998
-
Projectivity and isomorphism of strictly simple algebras.
Algebra Universalis.
45-56.
1998
-
Self-rectangulating varieties of type 5.
International Journal of Algebra and Computation.
511-540.
1997
-
The class of prime semilattices is not finitely axiomatizable.
Semigroup Forum.
133-134.
1997
-
A characterization of minimal locally finite varieties.
Transactions of the American Mathematical Society.
1749-1768.
1997
-
A Hamiltonian property for nilpotent algebras.
Algebra Universalis.
403-421.
1997
- Algebras whose subalgebras and reducts are trivial. Acta Scientiarum Mathematicarum. 379-381. 1997
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Locally solvable factors of varieties.
Proceedings of the American Mathematical Society.
3619-3625.
1996
-
Cardinality bounds for subdirectly irreducible algebras.
Journal of Pure and Applied Algebra.
293-312.
1996
-
Bialgebraic contexts from dualities.
Journal- Australian Mathematical Society Series a.
389-404.
1996
-
Critical algebras and the frattini congruence .2..
Bulletin of the Australian Mathematical Society.
91-100.
1996
-
A QUASI-AFFINE REPRESENTATION.
International Journal of Algebra and Computation.
673-702.
1995
-
VARIETIES WITH A DIFFERENCE TERM.
Journal of Algebra.
926-960.
1995
-
EVERY NEARLY IDEMPOTENT PLAIN ALGEBRA GENERATES A MINIMAL VARIETY.
Algebra Universalis.
322-325.
1995
- Minimal clones with abelian representations. Acta Scientiarum Mathematicarum. 59-76. 1995
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SEMILATTICE MODES .1. THE ASSOCIATED SEMIRING.
Algebra Universalis.
220-272.
1995
-
SEMILATTICE MODES .2. THE AMALGAMATION PROPERTY.
Algebra Universalis.
273-303.
1995
-
Inherently Nonfinitely Based Solvable Algebras.
Canadian Mathematical Bulletin.
514-521.
1994
-
CONGRUENCE SEMIMODULAR VARIETIES .1. LOCALLY FINITE VARIETIES.
Algebra Universalis.
224-269.
1994
-
CONGRUENCE SEMIMODULAR VARIETIES .2. REGULAR VARIETIES.
Algebra Universalis.
270-296.
1994
-
AN ORDER-THEORETIC PROPERTY OF THE COMMUTATOR.
International Journal of Algebra and Computation.
491-533.
1993
-
CONGRUENCE PERMUTABLE AND CONGRUENCE 3-PERMUTABLE LOCALLY FINITE VARIETIES.
Journal of Algebra.
36-49.
1993
-
NATURAL EXAMPLES OF QUASIVARIETIES WITH EDPM.
Algebra Universalis.
598-600.
1993
-
Commutator theory for relatively modular quasivarieties.
Transactions of the American Mathematical Society.
465-502.
1992
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FINITE-ALGEBRAS THAT GENERATE AN INJECTIVELY COMPLETE MODULAR VARIETY.
Bulletin of the Australian Mathematical Society.
303-324.
1991
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Type Preservation In Locally Finite Varieties with the CEP.
Canadian Journal of Mathematics.
748-769.
1991
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CONGRUENCE LOWER SEMIMODULARITY AND 2-FINITENESS IMPLY CONGRUENCE MODULARITY.
Algebra Universalis.
1-11.
1991
-
RESIDUAL BOUNDS FOR VARIETIES OF MODULES.
Algebra Universalis.
448-452.
1991
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Atomicity And Nilpotence.
Canadian Journal of Mathematics.
365-382.
1990
-
RELATIVELY CONGRUENCE DISTRIBUTIVE SUBQUASIVARIETIES OF A CONGRUENCE MODULAR VARIETY.
Bulletin of the Australian Mathematical Society.
87-96.
1990
-
ON THE RELATIONSHIP BETWEEN AP, RS AND CEP.
Proceedings of the American Mathematical Society.
827-839.
1989
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On the relationship between AP, RS and CEP.
Proceedings of the American Mathematical Society.
827-827.
1989
Background
education and training
- Ph.D., University of California-Berkeley 1988
- M.S., University of California-Riverside 1983
- B.S., University of California-Riverside 1982