Modularity and distributivity of the lattice of $\Sigma$-closed subsets of an algebraic structure

Chajda, Ivan, and Emanovský, Petr. "Modularity and distributivity of the lattice of $\Sigma $-closed subsets of an algebraic structure." Mathematica Bohemica 120.2 (1995): 209-217. <http://eudml.org/doc/247812>.

@article{Chajda1995,
abstract = {Let $\mathcal \{A\} =(A,F,R)$ be an algebraic structure of type $\tau $ and $\Sigma $ a set of open formulas of the first order language $L(\tau )$. The set $C_\Sigma (\mathcal \{A\})$ of all subsets of $A$ closed under $\Sigma $ forms the so called lattice of $\Sigma $-closed subsets of $\mathcal \{A\}$. We prove various sufficient conditions under which the lattice $C_\Sigma (\mathcal \{A\})$ is modular or distributive.},
author = {Chajda, Ivan, Emanovský, Petr},
journal = {Mathematica Bohemica},
keywords = {closure system; modular lattice; distributive lattice; lattices of Sigma- closed subsets},
language = {eng},
number = {2},
pages = {209-217},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modularity and distributivity of the lattice of $\Sigma $-closed subsets of an algebraic structure},
url = {http://eudml.org/doc/247812},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Chajda, Ivan
AU - Emanovský, Petr
TI - Modularity and distributivity of the lattice of $\Sigma $-closed subsets of an algebraic structure
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 2
SP - 209
EP - 217
AB - Let $\mathcal {A} =(A,F,R)$ be an algebraic structure of type $\tau $ and $\Sigma $ a set of open formulas of the first order language $L(\tau )$. The set $C_\Sigma (\mathcal {A})$ of all subsets of $A$ closed under $\Sigma $ forms the so called lattice of $\Sigma $-closed subsets of $\mathcal {A}$. We prove various sufficient conditions under which the lattice $C_\Sigma (\mathcal {A})$ is modular or distributive.
LA - eng
KW - closure system; modular lattice; distributive lattice; lattices of Sigma- closed subsets
UR - http://eudml.org/doc/247812
ER -