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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A characterization of function rings with Boolean domain

Author: Andrew B. Carson
Journal: Proc. Amer. Math. Soc. 121 (1994), 13-24
MSC: Primary 16S60; Secondary 03C60
MathSciNet review: 1174487
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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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Keywords: Function rings, Boolean domain, indecomposable range, characterization
Article copyright: © Copyright 1994 American Mathematical Society