A family of varieties of pseudosemilattices

Abstract

In K. Auinger and L. Oliveira (Studia Sci Math Hung 50:207–241, 2013), a basis of identities $\{u_n\approx v_n\,\mid \; n\ge 2\}$ for the variety SPS of all strict pseudosemilattices was determined. Each one of these identities $u_n\approx v_n$ 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 one of them is defined by a single identity also with 2-content $D_n$. In the literature there is only reference to the variety of all pseudosemilattices or to one of the nine varieties of strict pseudosemilattices (eight of them being the varieties of normal bands). This paper contributes with a countably infinite list of varieties of pseudosemilattices strictly containing SPS. We end this paper with the study of the inclusion relation between the varieties from this list.