A family of varieties of pseudosemilattices

Abstract

In [3], a basis of identities {u_n = v_n | n\geq 2} for the variety SPS of all strict pseudosemilattices was determined. Each one of these identities u_n = v_n has a peculiar 2-content D_n. In this paper we study the varieties of pseudosemilattices defined by sets of identities, all with 2-content the same D_n. 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 D_n. This paper ends with the study of the inclusion relation between the varieties of this family.