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Pseudocomplemented distributive lattices with small endomorphism monoids

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, New York 12561, USA;
V. Koubek
Affiliation:
MFF KU, Malostranské nám. 25, Praha 1, Czechoslovakia;
J. Sichler
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, CanadaR3T 2N2.
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Abstract

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By a result of K.B. Lee, the lattice of varieties of pseudo-complemented distributive lattices is the ω + 1 chain

where B−1, B0, B1 are the varieties formed by all trivial, Boolean, and Stone algebras, respectively. General theorems on relative universality proved in the present paper imply that there is a proper class of non-isomorphic algebras in B3 with finite endomorphism monoids, while every infinite algebra from B2 has infinitely many endomorphisms. The variety B4 contains a proper class of non-isomorphic algebras with endomorphism monoids consisting of the identity and finitely many right zeros; on the other hand, any algebra in B3 with a finite endomorphism monoid of this type must be finite.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 305 - 318
Copyright
Copyright © Australian Mathematical Society 1983

References

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