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

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.