The Structure of Pseudocomplemented Distributive Lattices. Ii: Congruence Extension and Amalgamation

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 ¿Sn, — lá«So), 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 «¿2 or n = w. For 3gn; in particular, we determine the finite algebras in Amal (3Sn). 1. The Congruence Extension Property. A class JT of algebras is said to satisfy the Congruence Extension Property if, given any algebra B and subalgebra A, both in Jf, and any congruence 0 on A, there is a congruence 0 on B such that the Received by the editors July 8, 1970. AMS 1970 subject classifications. Primary 06A35; Secondary 08A25,18A20,18A30,18C05.