Tensor products and the Loomis-Sikorski theorem for MV-algebras
type: Item
instance of: scholarly article
title: Tensor products and the Loomis-Sikorski theorem for MV-algebras
zbMATH Open document ID: 0926.06004
published in: Advances in Applied Mathematics
publication date: 1999-11-21T00:00:00Z
review text: 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.
reviewed by: C. S. Hoo
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 1295418
zbMATH Keywords: MV-tensor product
zbMATH Keywords: MV-algebras
zbMATH Keywords: semisimple algebras
zbMATH Keywords: generalization of the Loomis-Sikorski theorem
zbMATH Keywords: maximal ideals
zbMATH Keywords: tribe
author: Daniele Mundici
MaRDI profile type: Publication
full work available at URL: aama.1998.0631
OpenAlex ID: W1989551546
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DOI: 10.1006/AAMA.1998.0631
description: scientific article; zbMATH DE number 1295418