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Homomorphisms of distributive p-algebras with countably many minimal prime ideals

Published online by Cambridge University Press:  17 April 2009

M. E. Adams ,
V. Koubek  and
J. Sichler
M. E. Adams
Affiliation:
Department of Mathematics, State University of New York, New Paltz, NY 12561, U.S.A.
V. Koubek
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
J. Sichler
Affiliation:
MFF KU, Malostranské nám. 25, 118 00 Praha 1, Czechoslovakia
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Abstract

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According to a result of Lee, varieties of pseudocomplemented distributive lattices form an ω+1 chain in which is the trivial variety and is the variety of Boolean algebras. In the present paper it is shown that the variety contains an almost universal subcategory B in which the members of Hom(B,B') associated with minimal prime ideals of B form a countably infinite set for any B,B' ∈ B. In particular, B3contains arbitrarily large algebras whose nontrivial endomorphisms form the countably infinite right zero semigroup. Our earlier results concerning categorical properties of varieties of pseudocomplemented distributive lattices show that no further reduction of the right zero count is possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 427 - 439
Copyright
Copyright © Australian Mathematical Society 1987

References

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