Natural dualities for quasivarieties generated by a finite commutative ring

Abstract

Let R be a finite commutative ring with identity. If the Jacobson radical of R annihilates itself, then the quasivariety generated by R is dually equivalent to a category of structured Boolean spaces obtained in a natural way from R. If on the other hand the radical of R does not annihilate itself, then no such natural dual equivalence is possible. To illustrate the first result, a dual equivalence for the quasivariety generated by the ring \( \Bbb Z _{p^2} \), where p is prime, is given.