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

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.