Relatively pseudocomplemented directoids. (English) Zbl 1212.06004

Chajda, I.

Commentat. Math. Univ. Carol. 50, No. 3, 349-358 (2009).

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

Keywords:

directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity