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 LŁukasiewicz, 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 σ-complete multiplicatively closed MV-algebras, and pointwise σ-complete MV-algebras of [0,1]-valued functions.

Tensor Products and the Loomis-Sikorski theorem for MV-algebras / D. MUNDICI. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - STAMPA. - 22:(1999), pp. 227-248. [10.1006/aama.1998.0631]

Tensor Products and the Loomis-Sikorski theorem for MV-algebras

MUNDICI, DANIELE
1999

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 LŁukasiewicz, 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 σ-complete multiplicatively closed MV-algebras, and pointwise σ-complete MV-algebras of [0,1]-valued functions.
1999
22
227
248
D. MUNDICI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/308241
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