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Free distributive P-algebras: a new approach†

Published online by Cambridge University Press:  18 May 2009

Tibor Katriňák
Tibor Katriňák
Affiliation:
KATČ MFF UK, Mlynská Dolina, 84215 Bratislava, Slovakia
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It is well known (Lee [13]) that the class of all distributive p-algebras B = Bω is a variety and that the class of all subvarieties of B forms a chain

where B-i is the trivial class, B0 is the class of Boolean algebras, and B1 is the class of Stone algebras.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998, pp. 333 - 342
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Balbes, R., Projective and injective distributive lattice, Pacific J. Math. 21 (1967), 405–420.CrossRefGoogle Scholar
2.Balbes, R. and Dwinger, Ph., Distributive lattices (Univ. Missouri Press, 1974).Google Scholar
3.Balbes, R. and Horn, A., Stone lattices, Duke Math. J. 37 (1970), 537–546.CrossRefGoogle Scholar
4.Berman, J. and Dwinger, Ph., Finitely generated pseudocomplemented distributive lattices, J. Austral. Math. Soc. 19 (1975), 238–246.CrossRefGoogle Scholar
5.Chen, C. C., Free Stone extensions of distributive lattice, Nanta Math. 2 (1965), 1–15.Google Scholar
6.Dean, R. A., Free lattices generated by partially ordered sets and preserving bounds, Canad. J. Math. 16 (1964), 136–148.CrossRefGoogle Scholar
7.Davey, B. A. and Goldberg, M. S., The free p-algebra generated by a distributive lattice, Algebra Univ. 11 (1980), 90–100.CrossRefGoogle Scholar
8.Grätzer, G., General lattice theory (Akademie-Verlag, 1978).CrossRefGoogle Scholar
9.Katriňák, T., Die freien Stoneschen Verbände und ihre Tripelcharakterisierung, Ada Math. Sci. Hungar. 23 (1970), 315–326.CrossRefGoogle Scholar
10.Katriňák, T., A new description of the free Stone algebra, Algebra Univ. 5 (1975), 179–189.CrossRefGoogle Scholar
11.Katriňák, T., Free p-algebras, Algebra Univ. 15 (1982), 176–186.CrossRefGoogle Scholar
12.Köhler, P., The triple method and free distributive pseudocomplemented lattices, Algebra Univ. 8 (1978), 139–150.CrossRefGoogle Scholar
13.Lee, K. B., Equational classes of distributive pseudocomplemented lattices, Canad. J. Math. 11 (1970), 881–891.CrossRefGoogle Scholar
14.Urquhart, A., Free distributive pseudo-complemented lattices, Algebra Univ. 3 (1973), 13–15.CrossRefGoogle Scholar
15.Wafker, P., Generalization of a theorem on distributive pseudocomplemented lattices, (preprint).Google Scholar