Coproducts of distributive lattice-based algebras

Journal article

This paper presents a systematic study of coproducts. This is carried out principally, but not exclusively, for finitely generated quasivarieties A that admit a (term) reduct in the variety D of bounded distributive lattices. In this setting, we present necessary and sufficient conditions on A for the forgetful functor UA from A to D to preserve coproducts. We also investigate the possible behaviours of UA as regards coproducts in A under weaker assumptions. Depending on the properties exhibited by the functor, different procedures are then available for describing these coproducts. We classify a selection of well–known varieties within our scheme, thereby unifying earlier results and obtaining some new ones.

Authors: Cabrer, L; Priestley, H

• Publication status: Published
• Publisher: Birkhauser Verlag AG
• Journal: ALGEBRA UNIVERSALIS
• Volume: 72
• Issue: 3
• Pages: 251-286
• Publication date: 2014-11-01
• DOI: 10.1007/s00012-014-0302-3
• ISSN: 0002-5240
• Language: English
• Keywords: piggyback duality; distributive lattices; natural duality; ordered algebras; functors preserving coproducts; coproducts