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Projective distributive p-algebras

Published online by Cambridge University Press:  17 April 2009

Alasdair Urquhart
Alasdair Urquhart
Affiliation:
Department of Philosophy, University of Toronto, Toronto M5S 1A1, Canada.
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Abstract

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A characterization of finite (weak) projectives in an equational class of distributive pseudocomplemented lattices is given. In the class of all such lattices, a finite lattice is projective if and only if its poset of join–irreducible elements forms a semilattice in which the minimal elements below the join of x and y are exactly the mininal elements below x or y. A similar condition works for any equational subclass.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 2 , October 1981 , pp. 269 - 275
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Davey, Brian A., “Subdirectly irreducible distributive double p-algebras”, Algebra Universalis 8 (1978), 73–88.CrossRefGoogle Scholar
[2]Davey, Brian A. and Goldberg, Moshe S., “The free p-algebra generated by a distributive lattice”, Algebra Universalis (to appear).Google Scholar
[3]Grätzer, George, Lattice theory. First concepts and distributive lattices (Freeman, San Francisco, 1971).Google Scholar
[4]Grätzer, George, General lattice theory (Mathematische Reihe, 52. Birkhauser Verlag, Basel, Stuttgard, 1978).CrossRefGoogle Scholar
[5]Kuratowski, Kazimierz, Topology, Volume I, new edition (Academic Press, New York, London; Panstwowe Wydawnictwo Naukowe, Warsaw; 1966).Google Scholar
[6]Priestley, H.A., “Representation of distributive lattices by means of ordered Stone spaces”, Bull. London Math. Soc. 2 (1970), 186–190.CrossRefGoogle Scholar
[7]Priestley, H.A., “Stone lattices: a topological approach”, Fund. Math. 84 (1974), 127–143.CrossRefGoogle Scholar
[8]Priestley, H.A., “The construction of spaces dual to pseudocomplemented distributive lattices”, Quart. J. Math. Oxford Ser. (2) 26 (1975), 215–228.CrossRefGoogle Scholar
[9]Urquhart, A., “Free distributive pseudo-complemented lattices”, Algebra Universalis 3 (1973), 13–15.CrossRefGoogle Scholar