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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received October 1, 2000; accepted in final form December 27, 2000.
Rights and permissions
About this article
Cite this article
Clark, D., Idziak, P., Sabourin, L. et al. Natural dualities for quasivarieties generated by a finite commutative ring. Algebra univers. 46, 285–320 (2001). https://doi.org/10.1007/PL00000344
Issue Date:
DOI: https://doi.org/10.1007/PL00000344