Congruences on pseudocomplemented semilattices
Zuzana Heleyova · Discussiones Mathematicae - General Algebra and Applications · 2000
It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B1 [5]. In this paper we give a partial solution to a more general question: Under what condition on a pseudocomplemented semilattice its congruence lattice is element of the variety Bn (n ‚ 2)? In the last section we widen the Sankappanavar’s result to obtain the description of pseudocomplemented semilattices with relative Stone congruence lattices. A partial solution of the description of pseudocomplemented semilattices with relative (Ln)-congruence lattices (n ‚ 2) is also given.