Distributive lattices with finite projective covers

Alan Day, Herbert S. Gaskill and Werner Poguntke

Vol. 81 (1979), No. 1, 45–59

DOI: 10.2140/pjm.1979.81.45

Abstract

A projective cover in a category, 𝒦, of algebras is a morphism ϕ : P → A where A,P ∈𝒦, P is projective in 𝒦 and no proper subalgebra of P has A as its direct image under ϕ. Projective covers of finite distributive lattices in the categories ℒ, of all lattices and ℒ_fin of all finite lattices are determined (when they exist).

Mathematical Subject Classification 2000

Primary: 06B25

Secondary: 06D05

Milestones

Received: 31 May 1978

Published: 1 March 1979