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Relatively pseudocomplemented directoids. (English) Zbl 1212.06004
Summary: The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called \(p\)-ideals.

MSC:
06A12 Semilattices
06D15 Pseudocomplemented lattices
08B10 Congruence modularity, congruence distributivity
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