Dualisability versus residual character: a theorem and a counterexample (Q886225)

A finite algebra \(A\) is inherently non-dualisable if there is no natural representation for the quasivariety \(\text{ISP}(B)\), where \(B\) is a finite algebra such that \(A\in \text{ISP}(B)\). In this paper the authors show that a finite algebra must be inherently non-dualisable if the variety that it generates is both residually large and congruence meet-semidistributive. Also, they give the first example of a finite dualisable algebra that generates a variety that is residually large.