Geodesic
Implication and equivalential reducts of basic algebras
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 2, pp. 21-36 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 03G25, 06C15, 06D35, 08A62
Keywords: Basic algebra; implication algebra; implication reduct; equivalential algebra; equivalential reduct 
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     title = {Implication and equivalential reducts of basic algebras},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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     volume = {49},
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Chajda, Ivan; Kolařík, Miroslav; Švrček, Filip. Implication and equivalential reducts of basic algebras. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 2, pp. 21-36. http://geodesic.mathdoc.fr/item/AUPO_2010_49_2_a1/