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Tensor Products and the Loomis–Sikorski Theorem for MV-Algebras

✍ Scribed by Daniele Mundici

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 159 KB
Volume: 22
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1998.0631

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✦ Synopsis

MV-algebras are the models of the time-honored equational theory of magnitudes with unit. Introduced by Chang as a counterpart of the infinite-valued sentential calculus of Łukasiewicz, they are currently investigated for their relations with AF C*-algebras, toric desingularizations, and lattice-ordered abelian groups. Using tensor products, in this paper we shall characterize multiplicatively closed MV-algebras. Generalizing work of Loomis and Sikorski, we shall investigate the relationships between -complete multiplicatively closed MV-algebras, w x and pointwise -complete MV-algebras of 0, 1 -valued functions.

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