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.
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.
Reviewer: R.Firlová (Havirov-Mesto)
MSC:
06A12 | Semilattices |
08B25 | Products, amalgamated products, and other kinds of limits and colimits |