A characterization of function rings with Boolean domain

Carson, Andrew B.

doi:10.1090/S0002-9939-1994-1174487-0

A characterization of function rings with Boolean domain
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by Andrew B. Carson

Proc. Amer. Math. Soc. 121 (1994), 13-24

DOI: https://doi.org/10.1090/S0002-9939-1994-1174487-0

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Abstract:

In §1 we characterize (effectively in terms of omitted logical types) those countable rings that can be represented as certain specified functions from their Boolean spectra to some member of a universal class of indecomposable rings that has the amalgamation property. In §2 we show that this characterization fails for uncountable rings and give an alternate (although less interesting) one that does hold for all cardinalities.

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