Implication and equivalential reducts of basic algebras
Ivan Chajda; Miroslav Kolařík; Filip Švrček
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)
- Volume: 49, Issue: 2, page 21-36
- ISSN: 0231-9721
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topChajda, Ivan, Kolařík, Miroslav, and Švrček, Filip. "Implication and equivalential reducts of basic algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.2 (2010): 21-36. <http://eudml.org/doc/116511>.
@article{Chajda2010,
abstract = {A term operation implication is introduced in a given basic algebra $\mathcal \{A\}$ and properties of the implication reduct of $\mathcal \{A\}$ are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of $\mathcal \{A\}$ and, if this partial order is linear, the algebra $\mathcal \{A\}$ can be reconstructed by means of its equivalential reduct.},
author = {Chajda, Ivan, Kolařík, Miroslav, Švrček, Filip},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Basic algebra; implication algebra; implication reduct; equivalential algebra; equivalential reduct; basic algebra; orthomodular lattice; MV-algebra; implication reduct; equivalential reduct; congruence property; implication basic algebra},
language = {eng},
number = {2},
pages = {21-36},
publisher = {Palacký University Olomouc},
title = {Implication and equivalential reducts of basic algebras},
url = {http://eudml.org/doc/116511},
volume = {49},
year = {2010},
}
TY - JOUR
AU - Chajda, Ivan
AU - Kolařík, Miroslav
AU - Švrček, Filip
TI - Implication and equivalential reducts of basic algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 2
SP - 21
EP - 36
AB - A term operation implication is introduced in a given basic algebra $\mathcal {A}$ and properties of the implication reduct of $\mathcal {A}$ are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of $\mathcal {A}$ and, if this partial order is linear, the algebra $\mathcal {A}$ can be reconstructed by means of its equivalential reduct.
LA - eng
KW - Basic algebra; implication algebra; implication reduct; equivalential algebra; equivalential reduct; basic algebra; orthomodular lattice; MV-algebra; implication reduct; equivalential reduct; congruence property; implication basic algebra
UR - http://eudml.org/doc/116511
ER -
References
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