Congruences on pseudocomplemented semilattices

• Autorzy: Zuzana Heleyová
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pseudocomplemented semilattice; congruence lattice; p-algebra; Stone algebra; (relative) (Lₙ)-lattice

Kategorie tematyczne

• 06A99: None of the above, but in this section
• 06D15: Pseudocomplemented lattices
• 08A30: Subalgebras, congruence relations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 219-231

Daty

wydano

2000

otrzymano

1998-10-27

poprawiono

1999-10-01

Twórcy

autor

Zuzana Heleyová

• 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).

Identyfikatory

DOI

10.7151/dmgaa.1019