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

DOI:
https://doi.org/10.1090/S0002-9947-1971-0274359-9

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 , 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

**) are described. The Amalgamation Property is shown to hold iff or . For does not satisfy the Amalgamation Property; the deviation is measured by a class Amal . The finite algebras in Amal are determined.**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0274359-9

Keywords:
Distributive lattice,
pseudocomplemented,
congruence,
amalgamation,
free product,
standard semigroup,
amalgamation class

Article copyright:
© Copyright 1971
American Mathematical Society