| Title:
|
Hu's Primal Algebra Theorem revisited (English) |
| Author:
|
Porst, Hans-E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
855-859 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lawvere theory |
| Keyword:
|
equivalence between varieties |
| Keyword:
|
Hu's theorem |
| Keyword:
|
primal algebra |
| Keyword:
|
Post algebras |
| MSC:
|
06B20 |
| MSC:
|
06D25 |
| MSC:
|
08A40 |
| MSC:
|
08B99 |
| MSC:
|
18C05 |
| idZBL:
|
Zbl 1048.08003 |
| idMR:
|
MR1800177 |
| . |
| Date available:
|
2009-01-08T19:08:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119217 |
| . |
| Reference:
|
[1] Balbes R., Dwinger Ph.: Distributive Lattices.University of Missouri Press, Missouri, 1974. Zbl 0321.06012, MR 0373985 |
| Reference:
|
[2] Borceux F.: Handbook of Categorical Algebra Vol. 2.Cambridge University Press, Cambridge, 1994. |
| Reference:
|
[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. Zbl 0532.08003, MR 0724265 |
| Reference:
|
[4] Hu T.K.: Stone duality for Primal Algebra Theory.Math. Z. 110 (1969), 180-198. Zbl 0175.28903, MR 0244130 |
| Reference:
|
[5] Hu T.K.: On the topological duality for Primal Algebra Theory.Algebra Universalis 1 (1971), 152-154. Zbl 0236.08005, MR 0294218 |
| Reference:
|
[6] Lawvere F.W.: Functorial semantics of algebraic theories.PhD thesis, Columbia University, 1963. Zbl 1062.18004, MR 0158921 |
| Reference:
|
[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. MR 1404941 |
| Reference:
|
[8] Porst H.-E.: Equivalence for varieties in general and for Bool in particular.to appear in Algebra Universalis. MR 1773936 |
| . |
