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Kearnes, Keith A

Professor

Positions

• Professor, Mathematics

Research Areas

• Algebra
• Combinatorics
• Logic

Research

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.

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.  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

• conference proceeding

  • Logic Colloquium 2004.  xii+220-xii+220. 2008
    

• journal article

  • 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
  • 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
  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
  Cube term blockers without finiteness.  Algebra Universalis. 437-459. 2017
  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
  Dualizable algebras with parallelogram terms.  Algebra Universalis. 497-539. 2016
  Growth rates of algebras, III: finite solvable algebras.  Algebra Universalis. 199-222. 2016
  GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS.  Journal of the Australian Mathematical Society. 56-94. 2016
  
  A FINITE BASIS THEOREM FOR DIFFERENCE-TERM VARIETIES WITH A FINITE RESIDUAL BOUND.  Transactions of the American Mathematical Society. 2115-2143. 2016
  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
  Jonsson posets and unary Jonsson algebras.  Algebra Universalis. 101-112. 2013
  The Shape of Congruence Lattices.  Memoirs of the American Mathematical Society. 1-+. 2013
  Commuting Polynomial Operations of Distributive Lattices.  Order: a journal on the theory of ordered sets. 245-269. 2012
  The 3rd International Conference on Boolean Algebra, Lattice Theory, Universal Algebra, Set Theory and Set-theoretical Topology-BLAST 2010.  Order: a journal on the theory of ordered sets. 229-230. 2012
  An easy test for congruence modularity.  Algebra Universalis. 375-392. 2012
  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
  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
  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
  p(n)-sequences of algebras with one fundamental operation.  Algebra Universalis. 69-75. 2007
  Quasivarieties of Modules Over Path Algebras of Quivers.  Studia Logica: an international journal for symbolic logic. 333-349. 2006
  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
  Minimal sets in finite rings.  Algebra Universalis. 81-109. 2004
  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
  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
  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.  The Journal of Symbolic Logic. 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
  Finite algebras of finite complexity.  Discrete Mathematics. 89-135. 1999
  A geometric consequence of residual smallness.  Annals of Pure and Applied Logic. 137-169. 1999
  A modification of Polin's variety.  Algebra Universalis. 229-231. 1999
  Finiteness properties of locally finite abelian varieties.  International Journal of Algebra and Computation. 157-168. 1999
  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 Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 379-381. 1997
  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 Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 59-76. 1995
  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
  FINITE-ALGEBRAS THAT GENERATE AN INJECTIVELY COMPLETE MODULAR VARIETY.  Bulletin of the Australian Mathematical Society. 303-324. 1991
  Type Preservation In Locally Finite Varieties with the CEP.  Canadian Journal of Mathematics. 748-769. 1991
  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
  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
  On the relationship between AP, RS and CEP.  Proceedings of the American Mathematical Society. 827-827. 1989
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Teaching

courses taught

• MATH 2001 - Introduction to Discrete Mathematics
  Primary Instructor - Spring 2019 / Spring 2021 / Fall 2021 / Fall 2023
  Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
• MATH 2135 - Introduction to Linear Algebra for Mathematics Majors
  Primary Instructor - Spring 2021
  Examines basic properties of systems of linear equations, vector spaces, inner products, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors and diagonalization. Intended for students who plan to major in Mathematics. Degree credit not granted for this course and MATH 2130 or APPM 3310. Formerly MATH 3135.
• MATH 3001 - Analysis 1
  Primary Instructor - Fall 2018 / Fall 2019
  Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
• MATH 4730 - Set Theory
  Primary Instructor - Fall 2019 / Fall 2023
  Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic and other topics chosen by the instructor. Same as MATH 5730.
• MATH 4820 - History of Mathematical Ideas
  Primary Instructor - Fall 2024
  Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820.
MATH 5730 - Set Theory
Primary Instructor - Fall 2019 / Fall 2023
Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic and other topics chosen by the instructor. Same as MATH 4730.
MATH 6000 - Model Theory
Primary Instructor - Spring 2020 / Spring 2024
Proves the compactness theorem, showing the essential finiteness of logical implication. Proves many basic properties of theories, showing how the syntactic form of statements influences their behavior w.r.t., different models. Finally, studies properties of elements that cannot be stated by a single formula (the type of the element) and shows it can be used to characterize certain models.
MATH 6020 - Category Theory
Primary Instructor - Fall 2024
Studies categories, functors, natural transformations, adjoints, and universal constructions. Special topics may include monads and their algebras, abelian categories, Kan extensions, or sheaves in geometry and logic. Instructor consent required for undergraduates.
MATH 6150 - Commutative Algebra
Primary Instructor - Fall 2020
Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals and Noetherian rings. Department enforced prerequisite: MATH 6140. Instructor consent required for undergraduates.
MATH 6270 - Theory of Groups
Primary Instructor - Fall 2021
Studies nilpotent and solvable groups, simple linear groups, multiply transitive groups, extensions and cohomology, representations and character theory, and the transfer and its applications. Department enforced prerequisites: MATH 6130 and MATH 6140. Instructor consent required for undergraduates.
MATH 6730 - Set Theory
Primary Instructor - Spring 2023
Presents cardinal and ordinal arithmetic, and basic combinatorial concepts, including stationary sets, generalization of Ramsey's theorem, and ultrafilters, consisting of the axiom of choice and the generalized continuum hypothesis. Department enforced prerequisites: MATH 4000 or MATH 5000 and MATH 4730 or MATH 5730. Instructor consent required for undergraduates.
MATH 8714 - Topics in Logic 1 and 2
Primary Instructor - Fall 2018
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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

awards and honors

• Traditional Fulbright Scholarship, conferred by Council for International Exchange of Scholars, 2010

International Activities

geographic focus

• Argentina  Country
• Austria  Country
• Canada  Country
• Colombia  Country
• Hungary  Country
Russian Federation  Country
Serbia  Country
... more

Other Profiles

ORCID iD

• http://orcid.org/0000-0002-0229-8504

Google Scholar

• https://scholar.google.com/citations?user=vdZ7FwIAAAAJ&hl=en&oi=ao

ResearchGate

• https://www.researchgate.net/profile/Keith_Kearnes