Properties of relatively pseudocomplemented directoids

Chajda, Ivan, Kolařík, Miroslav, and Švrček, Filip. "Properties of relatively pseudocomplemented directoids." Mathematica Bohemica 136.1 (2011): 9-23. <http://eudml.org/doc/197064>.

@article{Chajda2011,
abstract = {The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for relatively pseudocomplemented directoids. Hence, they can also be considered as residuated structures in a rather modified version. We also get two important congruence properties, namely congruence distributivity and $3$-permutability valid in the variety $\mathcal \{V\}$ of relatively pseudocomplemented directoids. Then we show some basic results connected with subdirect irreducibility in $\mathcal \{V\}$. Finally, we show another way how to introduce pseudocomplementation on directoids via relative pseudocomplementation.},
author = {Chajda, Ivan, Kolařík, Miroslav, Švrček, Filip},
journal = {Mathematica Bohemica},
keywords = {directoid; relatively pseudocomplemented directoid; congruence distributivity; $3$-permutability; residuated structure; adjointness property; variety; directoid; relatively pseudocomplemented directoid; variety; congruence distributivity; 3-permutability; residuated structure; adjointness property},
language = {eng},
number = {1},
pages = {9-23},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of relatively pseudocomplemented directoids},
url = {http://eudml.org/doc/197064},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Chajda, Ivan
AU - Kolařík, Miroslav
AU - Švrček, Filip
TI - Properties of relatively pseudocomplemented directoids
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 9
EP - 23
AB - The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for relatively pseudocomplemented directoids. Hence, they can also be considered as residuated structures in a rather modified version. We also get two important congruence properties, namely congruence distributivity and $3$-permutability valid in the variety $\mathcal {V}$ of relatively pseudocomplemented directoids. Then we show some basic results connected with subdirect irreducibility in $\mathcal {V}$. Finally, we show another way how to introduce pseudocomplementation on directoids via relative pseudocomplementation.
LA - eng
KW - directoid; relatively pseudocomplemented directoid; congruence distributivity; $3$-permutability; residuated structure; adjointness property; variety; directoid; relatively pseudocomplemented directoid; variety; congruence distributivity; 3-permutability; residuated structure; adjointness property
UR - http://eudml.org/doc/197064
ER -