A characterization of function rings with Boolean domain
Author:
Andrew B. Carson
Journal:
Proc. Amer. Math. Soc. 121 (1994), 1324
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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 R. Arens and I. Kaplansky, Topological representations of algebras, Trans. Amer. Math. Soc. 63 (1949), 457481. MR 0025453 (10:7c)
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 A. Carson, Representation of semisimple algebraic algebras, J. Algebra 24 (1973), 245257. MR 0309931 (46:9035)
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 , Selfinjective regular algebras and function rings, Algebra Universalis 29 (1992), 449454. MR 1170200 (93h:54012)
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 S. Comer, Monadic algebras with finite degree, Algebra Universalis 5 (1975), 313327. MR 0403965 (53:7774)
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 T. J. Jech, Abstract theory of abelian operator algebras: an application of forcing, Trans. Amer. Math. Soc. 289 (1985), 133162. MR 779056 (87f:03146)
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 , Booleanlinear spaces, Adv. Math. 81 (1990), 117197. MR 1055646 (91d:06003)
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 R. S. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc., vol. 70, Amer. Math. Soc., Providence, RI, 1967. MR 0217056 (36:151)
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 H. Werner, Discriminator algebras. Algebraic representation and model theoretic properties, Akademie Verlag, Berlin, 1978. MR 526402 (80f:08009)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199411744870
PII:
S 00029939(1994)11744870
Keywords:
Function rings,
Boolean domain,
indecomposable range,
characterization
Article copyright:
© Copyright 1994
American Mathematical Society
