A Note on Distributive Triples

• Autorzy: Marcin Łazarz
• Języki publikacji: EN

Abstrakty

EN

Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.

Słowa kluczowe

EN

Distributive triple; dually distributive triple; covering diamond

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2019
• Tom: 48
• Numer: 3
• Strony: 207-211

Daty

wydano

2019-10-30

Twórcy

autor

Marcin Łazarz

• University of Wrocław, Poland, Department of Logic and Methodology of Sciences

Bibliografia

• G. Birkhoff, Lattice Theory, American Mathematical Society Colloquium Publications, Vol. XXV, Providence, Rhode Island (1973).
• E. Fried, G. Grätzer, H. Lakser, Projective geometries as cover-preserving sublattices, Algebra Universalis, Vol. 27 (1990), pp. 270–278.
• G. Grätzer, General lattice theory, Birkhäuser, Basel, Stuttgart (1978).
• G. Grätzer, Lattice Theory: Foundation, Birkhäuser, Basel (2011).
• C. Herrmann, A. P. Huhn, Lattices of normal subgroups which are generated by frames, [in:] Proceedings of the Lattice Theory Colloquium, Szeged 1974, Colloq. Math. Soc. János Bolyai, 14, pp. 97–136, North-Holland, Amsterdam (1976).
• B. Jónsson, Equational Classes of Lattices, Mathematica Scandinavica, Vol. 22 (1968), pp. 187–196.
• M. Stern, Semimodular Lattices. Theory and Applications, Cambridge University Press (1999).

Identyfikatory

DOI

10.18778/0138-0680.48.3.04