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Some p-algebras and double p-algebras having only principal congruences

Published online by Cambridge University Press:  18 May 2009

R. Beazer
R. Beazer
Affiliation:
University of Glasgow, University Gardens, G12 8QW, Scotland
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In [6], Blyth and Varlet characterize those algebras having only principal congruences in some well known classes of algebras having distributive lattice reducts. In particular, they characterize those Stone algebras having only principal congruences. In this paper we characterize those quasi-modular p-algebras having only principal congruences and show on specializing that distributive p-algebras having only principal congruences can be described in exactly the same way as Blyth and Varlet described Stone algebras having the same property. The same problem is addressed for some distributive double p-algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 157 - 164
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Adams, M. E. and Beazer, R., Congruence properties of distributive double p-algebras Czechoslovak Math. J. 41 (1991), 216–231.CrossRefGoogle Scholar
2.Balbes, R. and Dwinger, P., Distributive Lattices,(University of Missouri Press, 1974).Google Scholar
3.Beazer, R., The determination congruence on double p-algebras, Algebra Universalis 6 (1976), 121–129.CrossRefGoogle Scholar
4.Beazer, R., Congruence uniform algebras with pseudocomplementation, Studia Sci. Math.Hungar 20 (1985), 43–48.Google Scholar
5.Beazer, R., Principal congruence properties of some algebras with pseudocomplementation Portugaliae Math,(to appear).Google Scholar
6.Blyth, T. S. and Varlet, J. C., Principal congruences on some lattice-ordered algebras, Discrete Math. 81 (1990), 323–329.CrossRefGoogle Scholar
7.Burris, S. and Sankappanavar, H. P., A course in universal algebra, Graduate Texts in Mathematics, (Springer-Verlag, 1981).CrossRefGoogle Scholar
8.Davey, B. A., Subdirectly irreducible distributive double p-algebras, Algebra Universalis 8 (1978), 73–88.CrossRefGoogle Scholar
9.Grätzer, G., General lattice theory,(Birkhäuser Verlag, 1978).CrossRefGoogle Scholar
10.Katriňnáak, T., Congruence extension property for distributive double p-algebras, Algebra Universalis 4 (1974), 273–276.Google Scholar
11.Katriňnáak, T., Subdirectly irreducible p-algebras, Algebra Universalis 9 (1979), 116–126.CrossRefGoogle Scholar
12.Katriňnáak, T., p-algebras, Colloq. Math. Soc. J. Bolyai, Szeged (1980), 549–573.Google Scholar