Hu's Primal Algebra Theorem revisited
Porst, Hans-Eberhard
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000), p. 855-859 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2000-01-01
Classification:  06B20,  06D25,  08A40,  08B99,  18C05
@article{119217,
     author = {Hans-Eberhard Porst},
     title = {Hu's Primal Algebra Theorem revisited},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {41},
     year = {2000},
     pages = {855-859},
     zbl = {1048.08003},
     mrnumber = {1800177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119217}
}
Porst, Hans-Eberhard. Hu's Primal Algebra Theorem revisited. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 855-859. http://gdmltest.u-ga.fr/item/119217/

Balbes R.; Dwinger Ph. Distributive Lattices, University of Missouri Press, Missouri, 1974. | MR 0373985 | Zbl 0321.06012

Borceux F. Handbook of Categorical Algebra Vol. 2, Cambridge University Press, Cambridge, 1994.

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. | MR 0724265 | Zbl 0532.08003

Hu T.K. Stone duality for Primal Algebra Theory, Math. Z. 110 (1969), 180-198. (1969) | MR 0244130 | Zbl 0175.28903

Hu T.K. On the topological duality for Primal Algebra Theory, Algebra Universalis 1 (1971), 152-154. (1971) | MR 0294218 | Zbl 0236.08005

Lawvere F.W. Functorial semantics of algebraic theories, PhD thesis, Columbia University, 1963. | MR 0158921 | Zbl 1062.18004

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. | MR 1404941

Porst H.-E. Equivalence for varieties in general and for Bool in particular, to appear in Algebra Universalis. | MR 1773936