The Loomis--Sikorski Theorem for $EMV$-algebras

Anatolij Dvurečenskij; Omid Zahiri

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arXiv · 1707.00270

The Loomis--Sikorski Theorem for $EMV$-algebras

Anatolij Dvurečenskij·Omid Zahiri

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Abstract

Recently, in [DvZa], we have introduced $EMV$-algebras which resemble $MV$-algebras but the top element is not guaranteed for them. For $σ$-complete $EMV$-algebras, we prove an analogue of the Loomis--Sikorski Theorem showing that every $σ$-complete $EMV$-algebra is a $σ$-homomorphic image of an $EMV$-tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological properties of the state-morphism space and the space of maximal ideals are established.

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BibTeX RIS

Anatolij Dvurečenskij, Omid Zahiri. 2017-07-02. The Loomis--Sikorski Theorem for $EMV$-algebras. https://arxiv.org/abs/1707.00270

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