A family of varieties of pseudosemilattices

Abstract

In [3], a basis of identities {un ≈ vn | n ≥ 2} for the variety SPS of all strict pseudosemilattices was determined. Each one of these identities un ≈ vn has a peculiar 2-content Dn. In this paper we study the varieties of pseudosemilattices defined by sets of identities, all with 2-content the same Dn. We present here the family of all these varieties and show that each variety from this family is defined by a single identity also with 2-content Dn. This paper ends with the study of the inclusion relation between the varieties of this family.

Uniform Bands

“…It was shown that the classes of regular solid idempotent algebras and of pseudo-semilattices each form a variety [1,18]. The lattice of varieties of pseudo-semilattices was investigated extensively in [19]. The variety of bands is a subvariety of the variety of regular solid idempotent algebras; unlike the variety of all bands, the latter variety has a lattice of subvarieties that is of the power of the continuum (see the final remarks of [22, § 5]).…”