Research Information
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•Primary areas of interest:  Algebra, Logic, Combinatorics
• Member of editorial board for:  
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Students (for Honors, Master's, or PhD degree)
• Gena Boercker Pass, M.S. 2000, Thesis title: Irreducible sets in the Post varieties.
• Leanne Conaway, M.S. 2000, Thesis title: Minimal sets in finite rings.
• Matthew Nickodemus , Ph.D. 2007, Thesis title: Natural dualities for finite groups with abelian Sylow subgroups.
• Joshua Sanders, M.A. 2008.
• Yingwei Li, M.A. 2010, Thesis title: N-bounded varieties.
• Jason Hill, M.A. 2010.
• Young Jo Kwak, M.A. 2003, Ph.D. 2010, Thesis title: Automorphisms of some combinatorially defined Lie algebras over GF(2).
• Joshua Wiscons, Ph.D. 2011, Thesis title: Moufang sets of finite Morley rank.
• Matthew Moore, M.A. 2010, Ph.D. 2013, Thesis title: The undecidability of the definability of principal subcongruences.
• Andrew Moorhead, M.A. 2011, Ph.D. 2017, Thesis title: Higher commutator theory for congruence modular varieties.
• Kevin Berg, M.A. 2015, Ph.D. 2019, Thesis title: The complexity of homomorphism factorization.
• Steven Weinell, M.A. 2016, Ph.D. 2019, Thesis title: On the descending central series of higher commutators.
• Mark Pullins, M.A. 2016, Ph.D. 2020, Thesis title: Generically 2-transitive algebraic group actions with Solvable Point Stabilizers.
• Jordan Dubeau, M.A. 2018, Ph.D. 2022, Thesis title: Jónsson Jónsson-Tarski algebras.
• Michael (Mick) Walker, Honors 2022, Thesis title: Model-theoretic limits and the Hrushovski construction.
• Connor Meredith, M.A. 2019. Master's thesis title: Neutrabelian algebras and the split centralizer condition.
   Ph.D. 2023, Thesis title: Nilpotence and dualizability of algebras of finite type.
• Maya Ornstein, M.A. 2019, Ph.D. 2023 (co-advised with Josh Grochow).
   Ph.D. Thesis title: GENeralizing DEcompositions of Representations: Transitioning from Representations to Visible Actions.
• Athbi Aljadi, M.A. 2023.
• Chase Meadors, Ph.D. (in progress).
• Khizar Pasha, Senior thesis (in progress).

Books

The following list of books is in reverse order of publication. Authors' names are in alphabetical order.

3. Keith A. Kearnes and Emil W. Kiss, The Shape of Congruence Lattices. Mem. Amer. Math. Soc. 222 (2013), no. 1046, viii+169 pp. (version 2.00, 1.1 MB), PDF file for preprint. (This is the December 2011 version, which supersedes the previously posted September 2006 version.)

2. The 3rd International Conference on Boolean Algebra, Lattice Theory, Universal Algebra, Set Theory and Set-theoretical Topology--BLAST 2010. Edited by John Harding, Bart Kastermans, Keith Kearnes, Donald Monk, Ágnes Szendrei, Order 29 (2012), no. 2.  Sharedit link.

1. Logic Colloquium 2004, Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. Edited by A. Andretta, K. Kearnes and D. Zambella. Lecture Notes in Logic, 29. Association of Symbolic Logic, Cambridge University Press, 2008.

Expository Articles

The Hungarian journal KöMal (Mathematical and Physical Journal for Secondary Schools) asked my coauthors and I to prepare an expository article on Gaussian primes and Dirichlet's Theorem on primes in arithmetic progression.

1. Keith A. Kearnes, Emil W. Kiss and Ágnes Szendrei, Gauss-egészek és Dirichlet tétele. Első rész. KöMal, March, 2010. PDF file for preprint.

2. Második rész. KöMal, April, 2010. PDF file for preprint.


Research Articles

The following list of papers is in reverse order of publication. Authors' names are in alphabetical order.

99. Keith A. Kearnes, Relative Maltsev definability of some commutator properties. Internat. J. Algebra Comput. 33 (2023), no. 3, 391-433. arxiv

98. Keith A. Kearnes, Ágnes Szendrei and Ross D. Willard, Correction to ``A finite basis theorem for difference-term varieties with a finite residual bound''. Trans. Amer. Math. Soc. Ser. B 9 (2022), 322-342. Open Access

97. Keith A. Kearnes, Ágnes Szendrei and Ross D. Willard, Characterizing the commutator in varieties with a difference term. Algebra Universalis 83 (2022), no. 2, Paper No. 17. arxiv   Sharedit link.

96. Keith A. Kearnes and Ágnes Szendrei, Ultralocally closed clones, J. Multiple-Valued Logic and Soft Computing. arxiv

95. Xavier Caicedo, Miguel Campercholi, Keith A. Kearnes, Pedro Sánchez Terraf, Ágnes Szendrei, Diego Vaggione, Every minimal dual discriminator variety is minimal as a quasivariety, Algebra Universalis 82 (2021), no. 2, Paper No. 36.  Sharedit link.

94. Keith A. Kearnes, Emil W. Kiss and Ágnes Szendrei, Minimal abelian varieties of algebras, I, Internat. J. Algebra Comput. 31 (2021), no. 2, 205--217. arxiv

93. Keith A. Kearnes, Connor Meredith Ágnes Szendrei, Neutrabelian algebras, Algebra Universalis 82 (2021), no. 1, Paper No. 13. arxiv   Sharedit link.

92. Keith A. Kearnes and Alexander Rasstrigin, Representing subalgebras as retracts of finite subdirect powers, Algebra Universalis 81: 46 (2020). arxiv   Sharedit link.

91. Pham Ngoc Ánh, Keith A. Kearnes, Ágnes Szendrei, Commutative rings whose principal ideals have unique generators. In: Facchini A., Fontana M., Geroldinger A., Olberding B. (eds) Advances in Rings, Modules and Factorizations. Rings and Factorizations 2018. Springer Proceedings in Mathematics & Statistics, vol 321. Springer, Cham (2020). arxiv (title changed)

90. Keith A. Kearnes and Ágnes Szendrei, Is supernilpotence super nilpotence? Algebra Universalis (2020) 81:3. arxiv   Sharedit link.

89. Jordan Dubeau and Keith A. Kearnes, An uncountable Jónsson algebra in a minimal variety. Proc. Amer. Math. Soc., 148 (2020), no. 4, 1765--1775. arxiv

88. Keith A. Kearnes, Extending UFD's to PID's without adding units. J. Commut. Algebra, 10 (2018), no. 3, 347--358. PDF file for preprint.

87. Keith A. Kearnes, Peter Mayr, Nik Ruškuc, Solvable quotients of subdirect products of perfect groups are nilpotent. Bull. Lond. Math. Soc., 50 (2018) 1016--1026. arxiv

86. Keith A. Kearnes, Relatively congruence modular quasivarieties of modules. Don Pigozzi on abstract algebraic logic, universal algebra, and computer science, 221--232, Outstanding Contributions to Logic, 16, Springer, Cham, 2018. arxiv

85. Keith A. Kearnes, Emil W. Kiss and Ágnes Szendrei, Varieties whose finitely generated members are free. Algebra Universalis 79 (2018), no. 2, 79:3. arxiv   Sharedit link.

84. Keith A. Kearnes, Ágnes Szendrei and Ross D. Willard, Simpler Maltsev conditions for (weak) difference terms in locally finite varieties. Algebra Universalis 78 (2017), no. 4, 555--561. PDF file for preprint.   Sharedit link.

83. Keith A. Kearnes and Ágnes Szendrei, Cube term blockers without finiteness. Algebra Universalis 78 (2017), no. 4, 437--459. arxiv   Sharedit link.

82. Keith A. Kearnes and Ágnes Szendrei, Dualizable algebras with parallelogram terms. Algebra Universalis 76 (2016), no. 4, 497--539. arxiv   Sharedit link.

81. Keith A. Kearnes, Ágnes Szendrei and Ross D. Willard, A finite basis theorem for finite algebras with a difference term. Trans. Amer. Math. Soc. 368 (2016), no. 3, 2115--2143. PDF file for preprint.

78-80. Keith A. Kearnes, Emil W. Kiss and Ágnes Szendrei, Growth rates of algebras, I (J. Aust. Math. Soc.), II (Internat. J. Algebra and Comput.), & III (Algebra Universalis, ( Sharedit link. )) (Click on the number of the paper you want.)

77. Keith A. Kearnes, Petar Marković, and Ralph N. McKenzie, Optimal strong Mal'cev conditions for omitting type 1 in locally finite varieties. Algebra Universalis 72 (2014), no. 1, 91--100. PDF file for preprint.  Sharedit link.

76. Georg Grasegger, Gábor Horváth and Keith A. Kearnes, Polynomial equivalence of finite rings. Journal of the Australian Mathematical Society. 96 (2014), no. 2, 244--257. PDF file for preprint.

75. Keith A. Kearnes and Greg Oman, Jónnson posets and Jónnson unary algebras. Algebra Universalis 69 (2013), no. 2, 101--112. PDF file for preprint.   Sharedit link.

74. Topaz Dent, Keith A. Kearnes and Ágnes Szendrei, An easy test for congruence modularity. Algebra Universalis 67 (2012), no. 4, 375--392. PDF file for preprint. Sharedit link.

73. Mike Behrisch, Miguel Couceiro, Keith A. Kearnes, Erkko Lehtonen and Ágnes Szendrei, Commuting polynomial operations of distributive lattices. Order 29 (2012), no. 2, 245--269. PDF file for preprint.  Sharedit link.

72. Keith A. Kearnes and Ágnes Szendrei, Clones of algebras with parallelogram terms. Internat. J. Algebra Comput. 22 (2012). PDF file for preprint.

71. Keith A. Kearnes and Greg Oman, Cardinalities of residue fields of Noetherian integral domains. Comm. Algebra 38 (2010), no. 8, 3580--3588. PDF file for preprint.

70. Keith A. Kearnes and Young Jo Kwak, Residually finite varieties of nonassociative algebras. Comm. Algebra 38 (2010), no. 8, 3705--3727. PDF file for preprint.

69. Keith A. Kearnes, An axiomatic formation that is not a variety. J. Group Theory 13 (2010), no. 2, 233--241. PDF file for preprint.

68. Keith A. Kearnes, On the functional completeness of simple tournaments. Algebra Universalis 61 (2009), no. 3-4, 475--478. PDF file for preprint.  Sharedit link.

67. Pawel Idziak, Keith A. Kearnes, Emil W. Kiss and Matthew A. Valeriote, Definable principal congruences and solvability. Ann. Pure Appl. Logic 57 (2009), 30--49. PDF file for preprint.

66. Keith A. Kearnes, Jason Shaw and Ágnes Szendrei, Clones of 2-step nilpotent groups. Algebra Universalis 59 (2008), no. 3.4, 491--512. PDF file for preprint.   Sharedit link.

65. Keith A. Kearnes and J. B. Nation, Axiomatizable congruence prevarieties. Algebra Universalis 59 (2008), no. 3-4, 323--335. PDF file for preprint. Sharedit link.

64. Keith A. Kearnes and Ágnes Szendrei, Clones closed under conjugation, I. Internat. J. Algebra Comput. 18 (2008), no. 1, 7--58. PDF file for preprint.

63. Keith A. Kearnes and Steven T. Tschantz Automorphism groups of squares and of free algebras. Internat. J. Algebra Comput. 17 (2007), no. 3, 461--505. PDF file for preprint.

62. Keith A. Kearnes and Adam W. Marczak, pn-sequences of algebras with one fundamental operation. Algebra Universalis 56 (2007), 69--75. PDF file for preprint.  Sharedit link.

61. Keith A. Kearnes, Quasivarieties of modules over path algebras of quivers. Studia Logica 83 (2006), 333--349. PDF file for preprint.  Sharedit link.

60. Keith A. Kearnes and Emil W. Kiss, The triangular principle is equivalent to the triangular scheme. Algebra Universalis 54 (2005), no. 3, 273--283. PDF file for preprint.  Sharedit link.

59. Keith A. Kearnes, Congruence lattices of locally finite algebras. Algebra Universalis 54 (2005), no. 2, 237--248. PDF file for preprint.  Sharedit link.

58. Keith A. Kearnes and Ágnes Szendrei, Clones of finite groups. Algebra Universalis 54 (2005), no. 1, 23--52. PDF file for preprint.   Sharedit link. Corrigendum (10/26/08).

57. Keith A. Kearnes and Ágnes Szendrei, Groups with identical subgroup lattices in all powers. J. Group Theory 7 (2004), no. 3, 385--402. PDF file for preprint.

56. LeAnne Conaway and Keith A. Kearnes, Minimal sets in finite rings. Algebra Universalis 51 (2004), 81--109. PDF file for preprint.  Sharedit link.

55. Keith A. Kearnes and Emil W. Kiss, Residual smallness and weak centrality. Internat. J. Algebra Comput. 13 (2003), 35--59. PDF file for preprint.

54. Keith A. Kearnes and Luis Sequeira, Hausdorff properties of topological algebras. Algebra Universalis 47 (2002), 343--366. PDF file for preprint.  Sharedit link.
Correction: Theorem 5 is missing "m_i(x,y,y,x) = x for all i". This is used only in Theorem 34, and the omission in Thm 5 does not invalidate Thm 34. (Added 1/10/11.)

53. Keith A. Kearnes, Emil W. Kiss, Ágnes Szendrei and Ross D. Willard, Chief factor sizes in finitely generated varieties. Canad. J. Math. 54 (2002), 736--756. PDF file for preprint.

52. Keith A. Kearnes, Congruence join semidistributivity is equivalent to a congruence identity. Algebra Universalis 46 (2001), 373--387. PDF file for preprint.  Sharedit link.

51. Keith A. Kearnes, Agnes Szendrei and Japheth Wood, Generating singular transformations. Semigroup Forum 63 (2001), 441--448. PDF file for preprint.  Sharedit link.

50. Keith A. Kearnes and Emil W. Kiss, Left and right nilpotence degree are independent. Contributions to General Algebra, 13 (Velké Karlovice, 1999/Dresden, 2000), 189--198, Heyn, Klagenfurt, 2001. PDF file for preprint.

49. G. Czédli, R. Halas, K. A. Kearnes, P. P. Pálfy, and Ágnes Szendrei, The join of two minimal clones and the meet of two maximal clones. Algebra Universalis 45 (2001), 161--178. PDF file for preprint.  Sharedit link.

48. Keith A. Kearnes and Ágnes Szendrei, Collapsing permutation groups. Algebra Universalis 45 (2001), 35--51. PDF file for preprint.  Sharedit link.

47. Keith A. Kearnes, Almost all minimal idempotent varieties are congruence modular. Algebra Universalis 44 (2000), 39--45. PDF file for preprint.  Sharedit link.

46. Keith A. Kearnes, Categorical quasivarieties via Morita equivalence. J. of Symbolic Logic. 65 (2000), 839--856. PDF file for preprint.

45. Keith A. Kearnes, A characterization of locally finite varieties that satisfy a nontrivial congruence identity. Algebra Universalis 42 (1999), 195--204. PDF file for preprint.  Sharedit link.

44. Keith A. Kearnes, Congruence modular varieties with small free spectra. Algebra Universalis 42 (1999), 165--181. PDF file for preprint.  Sharedit link.

43. Keith A. Kearnes and Ágnes Szendrei, The residual character of varieties generated by strictly simple term minimal algebras. Algebra Universalis 42 (1999), 269--292. PDF file for preprint.  Sharedit link.

42. Keith A. Kearnes and Matthew A. Valeriote, A modification of Polin's variety. Algebra Universalis 41 (1999), 229--231. PDF file for preprint. Sharedit link.

41. Keith A. Kearnes and Ágnes Szendrei, The classification of commutative minimal clones. Discuss. Math. Algebra Stochastic Methods 19 (1999), 147--178. PDF file for preprint.

40. Keith A. Kearnes, Subdirectly irreducible modes. Discuss. Math. Algebra Stochastic Methods 19 (1999), 129--145. PDF file for preprint.

39. Keith A. Kearnes and Ross D. Willard, Residually finite congruence meet semidistributive varieties of finite type have a finite residual bound. Proc. Amer. Math. Soc. 127 (1999), 2841--2850. PDF file for preprint.

38. Keith A. Kearnes and Emil W. Kiss, Finite algebras of finite complexity. Discrete Math. 207 (1999), 89--135. PDF file for preprint.

37. Keith A. Kearnes, Emil W. Kiss and Matthew A. Valeriote, A geometric consequence of residual smallness. Ann. Pure Appl. Logic 99 (1999), 137--169. PDF file for preprint.

36. Keith A. Kearnes and Ross D. Willard, Finiteness properties of locally finite abelian varieties. Internat. J. Algebra Comput. 9 (1999), 157--168. PDF file for preprint.

35. Keith A. Kearnes and Emil W. Kiss, Modularity prevents tails. Proc. Amer. Math. Soc. 127 (1999), 11--19. PDF file for preprint.

34. Keith A. Kearnes and Ágnes Szendrei, Projectivity and isomorphism of strictly simple algebras. Algebra Universalis 39 (1998), 45--56. PDF file for preprint.  Sharedit link.

33. Keith A. Kearnes and Ágnes Szendrei, The relationship between two commutators. Internat. J. Algebra Comput. 8 (1998), 497--531. PDF file for preprint.

32. Keith A. Kearnes, Emil W. Kiss and Matthew A. Valeriote, Minimal sets and varieties. Trans. Amer. Math. Soc. (1998), 1--41. PDF file for preprint.

31. Béla Csákány and Keith A. Kearnes, Algebras whose subalgebras and reducts are trivial. Acta Sci. Math. 63 (1997), 377--379.

30. Keith A. Kearnes and Ágnes Szendrei, Self-rectangulating varieties of type 5. Internat. J. Algebra Comput. 7 (1997), 511--540. PDF file for preprint.

29. Keith A. Kearnes, The class of prime semilattices is not finitely axiomatizable. Semigroup Forum 55 (1997), 133--134. PDF file for preprint. Sharedit link.

28. Keith A. Kearnes and Ágnes Szendrei, A characterization of minimal, locally finite varieties. Trans. Amer. Math. Soc. 349 (1997), 1749--1768. PDF file for preprint.

27. Keith A. Kearnes, A Hamiltonian property for nilpotent algebras. Algebra Universalis, 37 (1997), 403--421. PDF file for preprint.  Sharedit link.

26. Keith A. Kearnes, Critical algebras and the Frattini congruence, II. Bulletin of the Australian Mathematical Society 53 (1996), 91--100. PDF file for preprint.

25. Keith A. Kearnes and Frank Vogt, Bialgebraic contexts from dualities. Journal of the Australian Mathematical Society 60 (1996), 389--404. PDF file for preprint.

24. Keith A. Kearnes, Locally solvable factors of varieties. Proc. Amer. Math. Soc. 124 (1996), 3619--3625. PDF file for preprint.

23. Keith A. Kearnes, Cardinality bounds for subdirectly irreducible algebras. Journal of Pure and Applied Algebra 112 (1996), 293--312. PDF file for preprint.

22. Keith A. Kearnes, Idempotent simple algebras. in Logic and Algebra, Lecture Notes in Pure and Appl. Math. 180, 1996, 529--572. PDF file for preprint.

21. Keith A. Kearnes, Varieties with a difference term. Journal of Algebra 177 (1995), 926--960. PDF file for preprint.

20. Keith A. Kearnes, Minimal clones with abelian representations. Acta Sci. Math. 61 (1995), 59--76. PDF file for preprint.

19. Keith A. Kearnes, A quasi-affine representation. Internat. J. Algebra Comput. 5 (1995), 673--702. PDF file for preprint.

18. Keith A. Kearnes, Semilattice modes, II: the amalgamation property. Algebra Universalis 34 (1995), 273--303. PDF file for preprint.  Sharedit link.

17. Keith A. Kearnes, Semilattice modes, I: the associated semiring. Algebra Universalis 34 (1995), 220--272. PDF file for preprint. Sharedit link.

16. Keith A. Kearnes, Every nearly idempotent plain algebra generates a minimal variety. Algebra Universalis 34 (1995), 322--325. PDF file for preprint. Sharedit link.

15. Ralph Freese, Keith A. Kearnes and J. B. Nation, Congruence lattices of congruence semidistributive algebras. in ``Lattice Theory and its Applications'', Heldermann Verlag, 1995, 63--78. PDF file for preprint.

14. Keith A. Kearnes and Ross D. Willard, Inherently nonfinitely based solvable algebras. Canadian Math. Bulletin 37 (1994), 514--521. PDF file for preprint.

13. Paolo Aglianò and Keith A. Kearnes, Congruence semimodular varieties II: regular varieties. Algebra Universalis 32 (1994), 270--296. PDF file for reprint.  Sharedit link.

12. Paolo Aglianò and Keith A. Kearnes, Congruence semimodular varieties I: locally finite varieties. Algebra Universalis 32 (1994), 224--269. PDF file for reprint.  Sharedit link.

11. Keith A. Kearnes, Natural examples of quasivarieties with EDPM. Algebra Universalis 30 (1993), 598--600. PDF file for preprint.  Sharedit link.

10. Keith A. Kearnes, An order-theoretic property of the commutator. Internat. J. Algebra Comput. 3 (1993), 491--533. PDF file for preprint.

9. Keith A. Kearnes, Congruence permutable and congruence 3-permutable locally finite varieties. Journal of Algebra 156 (1993), 36--49. PDF file for preprint.

8. Keith A. Kearnes and Ralph N. McKenzie, Commutator theory for relatively modular quasivarieties. Trans. Amer. Math. Soc. 331 (1992), 465--502.

7. Keith A. Kearnes, Type preservation in locally finite varieties with the CEP. Canadian Journal of Mathematics 43 (1991), 748--769.

6. Keith A. Kearnes, Finite algebras that generate an injectively complete variety. Bulletin of the Australian Mathematical Society 44 (1991), 303--324.

5. Keith A. Kearnes, Residual bounds for varieties of modules. Algebra Universalis 28 (1991), 448--452. PDF file for reprint.  Sharedit link.

4. Keith A. Kearnes, Congruence lower semimodularity and 2-finiteness imply congruence modularity. Algebra Universalis 28 (1991), 1--11. PDF file for reprint.  Sharedit link.

3. Keith A. Kearnes, Relatively congruence distributive subquasivarieties of a congruence modular variety. Bulletin of the Australian Mathematical Society 41 (1990), 87--96.

2. Keith A. Kearnes, Atomicity and nilpotence. Canadian Journal of Mathematics 42 (1990), 1--18.

1. Keith A. Kearnes, On the relationship between AP, RS and CEP. Proc. Amer. Math. Soc. 105 (1989), 827--839.


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