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Tensor products and the Loomis-Sikorski theorem for MV-algebras. (English) Zbl 0926.06004
The author defines the MV-tensor product of MV-algebras. However, since it is possible for a semisimple MV-algebra to have a tensor product with itself which is non-semisimple, he restricts himself to semisimple algebras and defines their semisimple tensor product, and gives a way to visualize it in terms of separating subalgebras of the algebra of continuous $$[0,1]$$-valued functions on the set of maximal ideals. If the algebra is also what he calls multiplicative, he defines a natural product on it. He proves a generalization of the Loomis-Sikorski theorem, namely:
Theorem. Let $$A$$ be a $$\sigma$$-complete MV-algebra and let $$X$$ be the set of maximal ideals. Then there is a tribe $${\mathcal F}$$ over $$X$$ and a $$\sigma$$-homomorphism $$\eta$$ of $${\mathcal F}$$ onto $$A$$. In fact, if $$A$$ is also multiplicative, then $${\mathcal F}$$ can be chosen to be closed under pointwise multiplication and $$\eta$$ is a homomorphism from this to the natural multiplication.
Reviewer: C.S.Hoo (Edmonton)

##### MSC:
 06D35 MV-algebras 46L05 General theory of $$C^*$$-algebras 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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##### References:
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