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    Davey, B. A. Haviar, M. and Priestley, H. A. 2016. Bohr Compactifications of Algebras and Structures. Applied Categorical Structures,


    KELAREV, A. V. YEARWOOD, J. L. and ZI, LIFANG 2013. OPTIMAL REES MATRIX CONSTRUCTIONS FOR ANALYSIS OF DATA. Journal of the Australian Mathematical Society, Vol. 92, Issue. 03, p. 357.


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    KELAREV, A. V. WATTERS, P. and YEARWOOD, J. L. 2009. REES MATRIX CONSTRUCTIONS FOR CLUSTERING OF DATA. Journal of the Australian Mathematical Society, Vol. 87, Issue. 03, p. 377.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 85, Issue 1
  • August 2008, pp. 59-74

PRINCIPAL AND SYNTACTIC CONGRUENCES IN CONGRUENCE-DISTRIBUTIVE AND CONGRUENCE-PERMUTABLE VARIETIES

  • BRIAN A. DAVEY (a1), MARCEL JACKSON (a2), MIKLÓS MARÓTI (a3) and RALPH N. MCKENZIE (a4)
  • DOI: http://dx.doi.org/10.1017/S144678870800061X
  • Published online: 01 August 2008
Abstract
Abstract

We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite.

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Copyright
Corresponding author
For correspondence; e-mail: m.g.jackson@latrobe.edu.au
Footnotes
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The second author was supported by ARC Discovery Project Grant DP0342459. The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 37877 and T 48809.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. Almeida and P. Weil , ‘Relatively free profinite monoids: an introduction and examples’, in: Semigroups, Formal Languages and Groups, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 466 (ed. J. Fountain) (Kluwer, Dordrecht, 1995), pp. 73117.

[2]K. A. Baker , G. F. McNulty and J. Wang , ‘An extension of Willard’s finite basis theorem: congruence meet-semidistributive varieties of finite critical depth’, Algebra Universalis 52 (2005), 289302.

[3]K. A. Baker and J. Wang , ‘Approximate distributive laws and finite equational bases for finite algebras in congruence-distributive varieties’, Algebra Universalis 54 (2005), 385396.

[4]S. Burris and H. P. Sankappanavar , A Course in Universal Algebra, Graduate Texts in Mathematics, 78 (Springer, Berlin, 1980).

[5]T. H. Choe , ‘Zero-dimensional compact associative distributive universal algebras’, Proc. Amer. Math. Soc. 42 (1974), 607613.

[6]D. M. Clark , B. A. Davey , R. S. Freese and M. Jackson , ‘Standard topological algebras: syntactic and principal congruences and profiniteness’, Algebra Universalis 52 (2004), 343376.

[8]D. M. Clark , B. A. Davey , M. Jackson and J. G. Pitkethly , ‘The axiomatizability of topological prevarieties’, Adv. Math. 218 (2008), 16041653.

[9]D. J. Clinkenbeard , ‘Simple compact topological lattices’, Algebra Universalis 9 (1979), 322328.

[13]P. Johnstone , Stone Spaces (Cambridge University Press, Cambridge, 1982).

[15]R. McKenzie , ‘Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties’, Algebra Universalis 8 (1978), 336348.

[16]R. McKenzie , ‘The residual bound of a finite algebra is not computable’, Internat. J. Algebra Comput. 6 (1996), 2948.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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