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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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  • [1] R. Arens and I. Kaplansky, Topological representations of algebras, Trans. Amer. Math. Soc. 63 (1949), 457-481. MR 0025453 (10:7c)
  • [2] A. Carson, Representation of semi-simple algebraic algebras, J. Algebra 24 (1973), 245-257. MR 0309931 (46:9035)
  • [3] -, Model completions, ring representations and the topology of the Pierce sheaf, Pitman Res. Notes Math. Ser., vol. 209, Longman Sci. Tech., Essex, 1989.
  • [4] -, A characterization of rings of twisted functions, Illinois J. Math. (to appear).
  • [5] -, Rings that are not elementarily equivalent to a function ring, Comm. Algebra 12 (1990), 4225-4234. MR 1084447 (92a:03051)
  • [6] -, Self-injective regular algebras and function rings, Algebra Universalis 29 (1992), 449-454. MR 1170200 (93h:54012)
  • [7] C. Chang and H. Keisler, Model theory, second ed., Studies in Logic Found. Math., vol. 73, North-Holland, Amsterdam, 1977. MR 0532927 (58:27177)
  • [8] S. Comer, Monadic algebras with finite degree, Algebra Universalis 5 (1975), 313-327. MR 0403965 (53:7774)
  • [9] T. J. Jech, Abstract theory of abelian operator algebras: an application of forcing, Trans. Amer. Math. Soc. 289 (1985), 133-162. MR 779056 (87f:03146)
  • [10] -, Boolean-linear spaces, Adv. Math. 81 (1990), 117-197. MR 1055646 (91d:06003)
  • [11] R. S. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc., vol. 70, Amer. Math. Soc., Providence, RI, 1967. MR 0217056 (36:151)
  • [12] H. Werner, Discriminator algebras. Algebraic representation and model theoretic properties, Akademie Verlag, Berlin, 1978. MR 526402 (80f:08009)

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Keywords: Function rings, Boolean domain, indecomposable range, characterization
Article copyright: © Copyright 1994 American Mathematical Society

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