A Note on Distributive Triples
Bulletin of the Section of Logic (2019)
- Volume: 48, Issue: 3, page 207-211
- ISSN: 0138-0680
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topMarcin Łazarz. "A Note on Distributive Triples." Bulletin of the Section of Logic 48.3 (2019): 207-211. <http://eudml.org/doc/295557>.
@article{MarcinŁazarz2019,
abstract = {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.},
author = {Marcin Łazarz},
journal = {Bulletin of the Section of Logic},
keywords = {Distributive triple; dually distributive triple; covering diamond},
language = {eng},
number = {3},
pages = {207-211},
title = {A Note on Distributive Triples},
url = {http://eudml.org/doc/295557},
volume = {48},
year = {2019},
}
TY - JOUR
AU - Marcin Łazarz
TI - A Note on Distributive Triples
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 3
SP - 207
EP - 211
AB - 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.
LA - eng
KW - Distributive triple; dually distributive triple; covering diamond
UR - http://eudml.org/doc/295557
ER -
References
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- 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).
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