Implication and Equivalential Reducts of Basic Algebras
Ivan Chajda · Czech digital mathematics library · 2010
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.