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Boolean semigroup rings and exponentials of compact zero-dimensional spaces. (English) Zbl 0716.54006
Let X be a zero-dimensional compact Hausdorff space and let Clop(X) denote the Boolean ring of clopen subsets of X. The author proves that the Boolean ring Clop(exp X), where exp X is the space of all closed subsets of X endowed with the Vietoris topology, is isomorphic to the semigroup ring over the multiplicative semigroup of Clop(X) with coefficients in the two-element field \(F_ 2\). There are also investigated Boolean rings that can be written in the form \(F_ 2[H]\) for some semilattice H. In particular, it is shown that neither complete Boolean rings nor infinite direct products of Boolean rings are of that type.
Reviewer: A.Błaszczyk

MSC:
54B20 Hyperspaces in general topology
06E20 Ring-theoretic properties of Boolean algebras
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