J. Aust. Math. Soc.  74 (2003), 393-420
Transferring optimal dualities: theory and practice

B. A. Davey
  School of Mathematics
  La Trobe University
  VIC 3086
  Australia
  B.Davey@latrobe.edu.au
and
M. Haviar
  Department of Mathematics
  M. Bel University
  PdF, Ruzova 13
  974 01 Banska Bystrica
  Slovak Republic
  haviar@pdf.umb.sk


Abstract
Consider the quasi-variety $\boldsymbol{\mathscr{D}}$ generated by a finite algebra $\mathbf{\underline{D}}$ and assume that $\underset{\sim}{\mathbf{D}}$ yields a natural duality on $\boldsymbol{\mathscr{D}}$ based on $\mathbf{\underline{D}}$ which is optimal modulo endomorphisms. We show that, provided $\underset{\sim}{\mathbf{D}}$ satisfies certain minimality conditions, we can transfer this duality to a natural duality on $\boldsymbol{\mathscr{D}}$ based on $\mathbf{\underline{M}}$, which is also optimal modulo endomorphisms, for any finite algebra $\mathbf{\underline{M}}$ in $\boldsymbol{\mathscr{D}}$ that has a subalgebra isomorphic to $\mathbf{\underline{D}}$.
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