Principal congruences on pseudocomplemented semilattices (Q535107)

It is proved that every principal congruence \(\Theta (a,b)\) on a pseudocomplemented semilattice can be expressed as a relational product of three principal semilattice congruences whose entries are couples which are terms in \(a,b,a^*,b^*\). The proof of this exploits the theory of binary discriminator varieties presented in [\textit{I. Chajda, R. Halaš} and \textit{I. G. Rosenberg}, ``Ideals and the binary dicriminator in universal algebra'', Algebra Univers. 42, No.~4, 239--251 (1999; Zbl 0979.08001)].