δ-Ideals in pseudo-complemented distributive join-semilattices

The concept of a [Formula: see text]-ideal is introduced in a pseudo-complemented distributive join semilattice with 0 and some properties of these ideals are obtained. We also give a characterization for a pseudo-complemented distributive join-semilattice to be a Stone join-semilattice. Also, in a distributive join-semilattice a characterization for an ideal to be a [Formula: see text]-ideal is proved.

Pseudo-BCH Semilattices

In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.