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Some remarks on dualisability and endodualisability

Gouveia, M. J.; (previously Saramago, M. J.)

Algebra Universalis, 43 (2000), 197-212

The fundamental problem of dualisability and the particular problem of endodualisability are discussed. It is proved that every finite generating algebra of a quasivariety generated by a finite dualisable algebra $\m$ is also dualisable. The corresponding result for endodualisablity is true when $\m$ is subdirectly irreducible. Under special conditions, it is also proved that a finite algebra $\m$ is endodualisable if and only if any finite power $\m^n$ of $\m$ is endodualisable.