# Orthomodular lattices with fully nontrivial commutators

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 1, page 25-32
- ISSN: 0010-2628

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topMatoušek, Milan. "Orthomodular lattices with fully nontrivial commutators." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 25-32. <http://eudml.org/doc/247373>.

@article{Matoušek1992,

abstract = {An orthomodular lattice $L$ is said to have fully nontrivial commutator if the commutator of any pair $x,y \in L$ is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbertian lattices, etc.) within this class. We also show that the quasivariety in question is not a variety answering thus the question implicitly posed in [4].},

author = {Matoušek, Milan},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {orthomodular lattice; commutator; quasivariety; free lattices; orthomodular lattice; fully nontrivial commutator; Hilbert lattices},

language = {eng},

number = {1},

pages = {25-32},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Orthomodular lattices with fully nontrivial commutators},

url = {http://eudml.org/doc/247373},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Matoušek, Milan

TI - Orthomodular lattices with fully nontrivial commutators

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 33

IS - 1

SP - 25

EP - 32

AB - An orthomodular lattice $L$ is said to have fully nontrivial commutator if the commutator of any pair $x,y \in L$ is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbertian lattices, etc.) within this class. We also show that the quasivariety in question is not a variety answering thus the question implicitly posed in [4].

LA - eng

KW - orthomodular lattice; commutator; quasivariety; free lattices; orthomodular lattice; fully nontrivial commutator; Hilbert lattices

UR - http://eudml.org/doc/247373

ER -

## References

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- Pták P., Pulmannová S., Orthomodular structures as quantum logics, Kluwer Academic Publishers, Dordrecht/Boston/London, 1991. MR1176314
- Pulmannová S., Commutators in orthomodular lattices, Demonstratio Math. 18 (1985), 187-208. (1985) MR0816029

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