×

Congruences on pseudocomplemented semilattices. (English) Zbl 0988.06001

In the paper pseudocomplemented semilattices \(S\), i.e. algebras \((S;\wedge,^*,0)\), where \((S;\wedge,0)\) is a meet semilattices with 0 and \(a\wedge x=0\) iff \(x\leq a^*\), and their congruence lattices \(\text{Con} (S)\) are studied. Especially, the cases for which \(\text{Con} (S)\) belongs to \(B_n\), \(n\geq 2\), are investigated. Note that \(B_n\), \(-1\leq n\leq\omega\), is a complete list of varieties of distributive pseudocomplemented lattices (K. B. Lee, 1970).

MSC:

06A12 Semilattices
06D15 Pseudocomplemented lattices
PDFBibTeX XMLCite
Full Text: DOI Link