Regular Article: Tensor Products and the Loomis驴Sikorski Theorem for MV-Algebras

Authors:
Daniele Mundici
Affiliations:
Department of Computer Science, University of Milan, Via Comelico 39-41, 20135, Milan, Italyf1mundici@imiucca.csi.unimi.itf1
Venue:
Advances in Applied Mathematics
Year:
1999

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Abstract

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 Lukasiewicz, they are currently investigated for their relations with AFC*-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 @s-complete multiplicatively closed MV-algebras, and pointwise @s-complete MV-algebras of [0,1]-valued functions.