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Advances in Applied Mathematics
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Advances in Applied Mathematics
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Tensor Products and the Loomis–Sikorski Theorem for MV-Algebras

Tensor products and the Loomis-Sikorski theorem for MV-algebras
Authors: MUNDICI, DANIELE;

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

Abstract

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.

Country
Italy
Related Organizations
Keywords

Effect Algebra, MV-algebra, Mathematics, MV-algebras, General theory of \(C^*\)-algebras, semisimple algebras, MV-tensor product, tribe, maximal ideals, Applied Mathematics, Ordered abelian groups, Riesz groups, ordered linear spaces, generalization of the Loomis-Sikorski theorem

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
81
Top 10%
Top 1%
Top 10%
hybrid