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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1019,
author = {Zuzana Heleyov\'a},
title = {Congruences on pseudocomplemented semilattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {219-231},
zbl = {0988.06001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1019}
}
Zuzana Heleyová. Congruences on pseudocomplemented semilattices. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 219-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1019/
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