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Congruences on pseudocomplemented semilattices

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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.
Twórcy
  • College of Business and Management, Technical University, Technicka 2, 616 69 Brno, Czech Republic
Bibliografia
  • [1] G. Grätzer, General Lattice Theory, Birkhäuser-Verlag, Basel 1978.
  • [2] M. Haviar and T. Katrinák, Semi-discrete lattices with (Ln)-congruence lattices, Contribution to General Algebra 7 (1991), 189-195.
  • [3] K.B. Lee, Equational classes of distributive pseudo-complemented lattices, Canad. J. Math. 22 (1970), 881-891.
  • [4] H.P. Sankappanavar, Congruence lattices of pseudocomplemented semilattices, Algebra Universalis 9 (1979), 304-316.
  • [5] H.P. Sankappanavar, On pseudocomplemented semilattices with Stone congruence lattices, Math. Slovaca 29 (1979), 381-395.
  • [6] H.P. Sankappanavar, On pseudocomplemented semilattices whose congruence lattices are distributive, (preprint).
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1019
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