On covers of quasivarieties of p-algebras

TL;DR

This paper investigates the structure of quasivarieties of p-algebras, proving that each variety has a unique cover in the lattice of subquasivarieties, thus resolving a previously open problem.

Contribution

It provides a complete characterization of covers of varieties of p-algebras within the lattice of quasivarieties, answering an open question in the field.

Findings

Each variety of p-algebras has exactly one cover in the lattice.

The result resolves a problem posed by Kowalski and S{2}omczy4ska.

The paper advances understanding of the lattice structure of quasivarieties.

Abstract

This paper characterizes the covers of varieties of p-algebras in the lattice of quasivarieties of p-algebras. In particular, it is shown that every such variety has exactly one cover in the lattice of subquasivarieties. This answers a problem of Kowalski and S{\l}omczy\'nska.