c-ideals in complemented posets

Chajda, Ivan, Kolařík, Miroslav, and Länger, Helmut. "c-ideals in complemented posets." Mathematica Bohemica 149.3 (2024): 305-316. <http://eudml.org/doc/299499>.

@article{Chajda2024,
abstract = {In their recent paper on posets with a pseudocomplementation denoted by $*$ the first and the third author introduced the concept of a $*$-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.},
author = {Chajda, Ivan, Kolařík, Miroslav, Länger, Helmut},
journal = {Mathematica Bohemica},
keywords = {complemented poset; antitone involution; ideal; filter; ultrafilter; c-ideal; c-filter; c-condition; separation theorem},
language = {eng},
number = {3},
pages = {305-316},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {c-ideals in complemented posets},
url = {http://eudml.org/doc/299499},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Chajda, Ivan
AU - Kolařík, Miroslav
AU - Länger, Helmut
TI - c-ideals in complemented posets
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 3
SP - 305
EP - 316
AB - In their recent paper on posets with a pseudocomplementation denoted by $*$ the first and the third author introduced the concept of a $*$-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.
LA - eng
KW - complemented poset; antitone involution; ideal; filter; ultrafilter; c-ideal; c-filter; c-condition; separation theorem
UR - http://eudml.org/doc/299499
ER -