Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-03T08:23:54.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Universal varieties of distributive double p-algebras

Published online by Cambridge University Press:  18 May 2009

V. Koubek  and
J. Sichler
V. Koubek
Affiliation:
Mff ku, Malostranské Nám. 25, Praha 1, Czechoslovakia
J. Sichler
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An algebra (L; ν, ^, *, +, 0, 1) of type (2, 2, 1, 1, 0, 0) is a distributive double p-algebra provided (L; ν, ^, 0, 1) is a distributive (0, l)-lattice, and *, + are unary operations of pseudocomplementation, or dual pseudocomplementation, respectively: the operation * satisfies x<a* if and only if x^a = 0, while x>a+ holds if and only if xνa = 1.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 2 , July 1985 , pp. 121 - 131
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Adams, M. E., Koubek, V. and Sichler, J., Homomorphisms and endomorphisms of distributive lattices, to appear in Houston J. Math.Google Scholar
2.Adams, M. E., Koubek, V. and Sichler, J., Endomorphisms and homomorphisms of Heyting algebras, to appear in Algebra Universalis.Google Scholar
3.Adams, M. E. and Sichler, J., Endomorphism monoids of distributive double p-algebras, Glasgow Math. J. 20 (1979), 81–86.CrossRefGoogle Scholar
4.Beazer, R., The determination congruence on double p-algebras, Algebra Universalis 6 (1976), 121–129.CrossRefGoogle Scholar
5.Beazer, R., Personal communication (1983).Google Scholar
6.Davey, B., Subdirectly irreducible distributive double p-algebras, Algebra Universalis 8 (1978), 73–88.CrossRefGoogle Scholar
7.Davey, B. A. and Duffus, D., Exponentiation and duality, Ordered Sets, NATO Advanced Study Institutes Series 83 (D. Reidel, 1982), 43–95.CrossRefGoogle Scholar
8.Hedrlin, Z. and Pultr, A., On rigid undirected graphs, Canad. J. Math. 18 (1966), 1237–1242.CrossRefGoogle Scholar
9.Hedrlín, Z. and Pultr, A., On full embeddings of categories of algebras, Illinois J. Math. 10 (1966), 392–406.CrossRefGoogle Scholar
10.Hedrlin, Z. and Sichler, J., Any boundable binding category contains a proper class of mutually disjoint copies of itself, Algebra Universalis 1 (1971), 97–103.CrossRefGoogle Scholar
11.Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110–121.CrossRefGoogle Scholar
12.Katriňák, T., The injective double Stone algebras, Algebra Universalis 4 (1974), 259–267.CrossRefGoogle Scholar
13.Nachbin, L., Topology and Order (Van Nostrand, 1965).Google Scholar
14.Priestley, H. A., Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2 (1970), 186–190.CrossRefGoogle Scholar
15.Priestley, H. A., Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. (3) 24 (1972), 507–530.CrossRefGoogle Scholar
16.Priestley, H. A., The construction of spaces dual to pseudocomplemented distributive lattices, Quart. J. Math. Oxford Ser. (2) 26 (1975), 215–228.CrossRefGoogle Scholar
17.Priestley, H. A., Ordered sets and duality for distributive lattices, Proc. Conf. on Ordered Sets and their Applications, Lyon (1982), to appear.Google Scholar
18.Pultr, A. and Trnková, V., Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories (North-Holland, 1980).Google Scholar
19.Varlet, J., A regular variety of type (2, 2, 1, 1, 0, 0), Algebra Universalis 2 (1972), 218–223.CrossRefGoogle Scholar