Free products of pseudocomplemented semilattices
Let \({\mathcal K}\) be the variety of pseudocomplemented semilattices (PCSs in brief), let \(S\), \(S_i\in{\mathcal K}\), for \(i\in I\). Then \(S\) is a free product of \(S_i\) \((i\in I)\) if there exist embeddings \(\varphi_i: S_i\to S\) such that \(S\) is generated by the set \(\bigcup \{\varphi_i(S_i);\;i\in I\}\), and if \(T\in K\) and \(\psi_i:S_i\to T\) are homomorphisms then there exists a homomorphism \(\psi:S\to T\) such that \(\psi_i=\varphi_i \circ\psi\). It is the aim of the paper to provide a characterization of the free products of PCSs. To this end the authors exploit known results on free products of Boolean algebras. Moreover, they derive an alternative description of the free PCSs.
scientific article; zbMATH DE number 1445563