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Keywords:
Basic algebra; implication algebra; implication reduct; equivalential algebra; equivalential reduct
Basic algebra; implication algebra; implication reduct; equivalential algebra; equivalential reduct
Summary:
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.
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