Abstract: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.
Keywords: directoid, relative pseudocomplementation, filter, congruence distributivity, congruence weak regularity
AMS Subject Classification: 06A12 06D15 08B10