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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The structure of pseudocomplemented distributive lattices. II. Congruence extension and amalgamation


Authors: G. Grätzer and H. Lakser
Journal: Trans. Amer. Math. Soc. 156 (1971), 343-358
MSC: Primary 06.50
MathSciNet review: 0274359
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Abstract: This paper continues the examination of the structure of pseudocomplemented distributive lattices. First, the Congruence Extension Property is proved. This is then applied to examine properties of the equational classes $ {\mathcal{B}_n}, - 1 \leqq n \leqq \omega $, which is a complete list of all the equational classes of pseudocomplemented distributive lattices (see Part I). The standard semigroups (i.e., the semigroup generated by the operators H, S, and P) are described. The Amalgamation Property is shown to hold iff $ n \leqq 2$ or $ n = \omega $. For $ 3 \leqq n < \omega ,{\mathcal{B}_n}$ does not satisfy the Amalgamation Property; the deviation is measured by a class Amal $ ({\mathcal{B}_n})( \subseteq {\mathcal{B}_n})$. The finite algebras in Amal $ ({\mathcal{B}_n})$ are determined.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0274359-9
PII: S 0002-9947(1971)0274359-9
Keywords: Distributive lattice, pseudocomplemented, congruence, amalgamation, free product, standard semigroup, amalgamation class
Article copyright: © Copyright 1971 American Mathematical Society