Hu's Primal Algebra Theorem revisited

Hans-Eberhard Porst

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 855-859
  • ISSN: 0010-2628

Abstract

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It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.

How to cite

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Porst, Hans-Eberhard. "Hu's Primal Algebra Theorem revisited." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 855-859. <http://eudml.org/doc/248588>.

@article{Porst2000,
abstract = {It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.},
author = {Porst, Hans-Eberhard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lawvere theory; equivalence between varieties; Hu's theorem; primal algebra; Post algebras; Lawvere theory; equivalence between varieties; Hu's theorem; primal algebra; Post algebra},
language = {eng},
number = {4},
pages = {855-859},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hu's Primal Algebra Theorem revisited},
url = {http://eudml.org/doc/248588},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Porst, Hans-Eberhard
TI - Hu's Primal Algebra Theorem revisited
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 855
EP - 859
AB - It is shown how Lawvere's one-to-one translation between Birkhoff's description of varieties and the categorical one (see [6]) turns Hu's theorem on varieties generated by a primal algebra (see [4], [5]) into a simple reformulation of the classical representation theorem of finite Boolean algebras as powerset algebras.
LA - eng
KW - Lawvere theory; equivalence between varieties; Hu's theorem; primal algebra; Post algebras; Lawvere theory; equivalence between varieties; Hu's theorem; primal algebra; Post algebra
UR - http://eudml.org/doc/248588
ER -

References

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  1. Balbes R., Dwinger Ph., Distributive Lattices, University of Missouri Press, Missouri, 1974. Zbl0321.06012MR0373985
  2. Borceux F., Handbook of Categorical Algebra Vol. 2, Cambridge University Press, Cambridge, 1994. 
  3. Davey B.A., Werner H., Dualities and equivalences for varieties of algebras, in A.P. Huhn and E.T. Schmidt, editors, `Contributions to Lattice Theory' (Proc. Conf. Szeged 1980), vol. 33 of Coll. Math. Soc. János Bolyai, North-Holland, 1983, pp.101-275. Zbl0532.08003MR0724265
  4. Hu T.K., Stone duality for Primal Algebra Theory, Math. Z. 110 (1969), 180-198. (1969) Zbl0175.28903MR0244130
  5. Hu T.K., On the topological duality for Primal Algebra Theory, Algebra Universalis 1 (1971), 152-154. (1971) Zbl0236.08005MR0294218
  6. Lawvere F.W., Functorial semantics of algebraic theories, PhD thesis, Columbia University, 1963. Zbl1062.18004MR0158921
  7. McKenzie R., An algebraic version of categorical equivalence for varieties and more general algebraic theories, in A. Ursini and P. Agliano, editors, `Logic and Algebra', vol. 180 of Lecture Notes in Pure and Appl. Mathematics, Marcel Dekker, 1996, pp.211-243. MR1404941
  8. Porst H.-E., Equivalence for varieties in general and for Bool in particular, to appear in Algebra Universalis. MR1773936

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