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On affine completeness of distributive p-algebras

Published online by Cambridge University Press:  18 May 2009

Miroslav Haviar
Miroslav Haviar
Affiliation:
KATČ, MFF UK Mlynská Dolina, CS-842 15 Bratislava Czecho-Slovakia
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G. Grätzer in [4] proved that any Boolean algebra B is affine complete, i.e. for every n ≥ 1, every function f:Bn→B preserving the congruences of B is algebraic. Various generalizations of this result have been obtained (see [7]–[ll] and [2], [3]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 365 - 368
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Balbes, R. and Dwinger, P., Distributive lattices (Univ. Missouri Press, Columbia, Miss., 1974).Google Scholar
2.Beazer, R., Affine complete Stone algebras, Acta. Math. Acad. Sci. Hungar. 39 (1982), 169–174.CrossRefGoogle Scholar
3.Beazer, R., Affine complete double Stone algebras with bounded core, Algebra Universalis 16 (1983), 237–244.CrossRefGoogle Scholar
4.Grätzer, G., On Boolean functions (notes on Lattice theory II), Revue de Math. Pures et Appliquées 7 (1962), 693–697.Google Scholar
5.Grätzer, G., Boolean functions on distributive lattices, Ada Math. Acad. Sci. Hungar. 15 (1964), 195–201.CrossRefGoogle Scholar
6.Grätzer, G., Lattice theory. First concepts and distributive lattices (W. H. Freeman, San Francisco, 1971).Google Scholar
7.Hu, T.-K., Characterizations of algebraic functions in equational classes generated by independent primal algebras, Albegra Universalis 1 (1971), 187–191.CrossRefGoogle Scholar
8.Iskander, A. A., Algebraic functions on p-rings, Colloq. Math. 25 (1972), 37–42.CrossRefGoogle Scholar
9.Keimel, K. and Werner, H., Stone duality for varieties generated by quasi-primal algebras. Recent advances in the representation theory of rings and C*-algebras by continuous sections, (Sem. Tulane Univ. New Orleans La. 1973), Mem. Amer. Math. Soc. 148 (1974), 59–85.Google Scholar
10.Knoebel, R. A., Congruence-preserving functions in quasiprimal varieties, Algebra Universalis 4 (1974), 287–288.CrossRefGoogle Scholar
11.Pixley, A. F., Completeness in arithmetical algebras, Algebra Universalis 2 (1972), 179–196.CrossRefGoogle Scholar
12.Werner, H., Produkte von Kongruenzklassengeometrien universeller Algebren, Math. Z. 121 (1971), 111–140.CrossRefGoogle Scholar