| Abstract:
This is a report on the paper "Natural dualities for quasivarieties
generated by a finite commutative ring" by D. Clark, P. Idziak, L.
Sabourin, Cs. Szabo and R. Willard, Alg. Univ. 46(2001), 285-320.
Arens and Kaplansky (1968) developed a duality for ISP(F) for each
finite field F = GF(q). In the case of GF(2), this is just Stone
duality for Boolean algebras (a.k.a. Boolean rings). In this paper,
the authors prove that for a finite commutative ring R, ISP(R) has a
duality if and only if J^2(R) = 0. I discuss the special cases R =
Z_{p^2} and R = Z_{p^3}, showing how to dualize the first and
showing why the second is not dualizable.
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