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Amalgamation in pseudocomplemented semilattices. (English) Zbl 0738.06003

Lattices, semigroups, and universal algebra, Proc. Int. Conf., Lisbon/Port. 1988, 291-297 (1990).
[For the entire collection see Zbl 0724.00010.]
The author compares amalgamation properties of certain natural subclasses of the variety PCS of all pseudocomplemented semilattices with those of analogous subclasses of the variety DPCL of distributive pseudo- complemented lattices. He considers the classes \(B_ n\) of \(n\)-atom Boolean algebras \((n\geq0)\) within both PCS and DPCL. More precisely, he addresses the natural problem of the amalgamation status of the quasivarieties \(B_ n\subseteq \hbox{PCS}\). Most of the answers are derivable from known results. Further, he was left with the two quasivarieties \(B_ 1\), \(B_ 2\). The main result shows that they do not have the amalgamation property — in contrast to the DPCL setting.

MSC:

06A12 Semilattices
08B25 Products, amalgamated products, and other kinds of limits and colimits

Citations:

Zbl 0724.00010