algebra universalis

, Volume 35, Issue 2, pp 265–295 | Cite as

When is a natural duality ‘good’?

  • D. M. Clark
  • B. A. Davey


Building on the most current work in the theory of natural dualities, we continue the study of strong dualities for the quasi-variety generated by a finite algebra. We investigate ten different versions of what we would like to mean by a ‘good duality’. Each version concerns, among other things, a specific restriction on the type of the structures in the dual category which insures that the dual structures will in a useful sense be simple. Through each investigation we seek a theorem characterizing, in terms of finitely verifiable conditions, those finite algebras generating a quasi-variety which admits a strong duality meeting the given restrictions. Our study includes a careful treatment of coproducts, logarithmic dualities and strong dualities by various unary structures.

1991 Mathematics Subject Classification

08C05 08C15 18A40 

Key words and phrases

Duality theory injective natural duality strong duality congruence distributivity near unanimity 


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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • D. M. Clark
    • 1
  • B. A. Davey
    • 2
  1. 1.Mathematics and Computer ScienceSUNYCollege at New PaltzNew PaltzUSA
  2. 2.School of MathematicsLa Trobe UniversityBundooraAustralia

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