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Regular representations of semisimple MV-algebras by continuous real functions. (English) Zbl 0987.06010
With any topological space $$M$$ one can associate the MV-algebra $$A_1(M)$$ corresponding to the $$\ell$$-group of all continuous bounded real functions on $$M$$. If $$A$$ is an MV-algebra and $$M$$ a topological space, then an injective morphism $$\varphi \:A\to A_1(M)$$ will be called a representation of $$A$$ by continuous real functions. A representation is regular if it preserves the suprema (and the infima).
It is proved here that for any semisimple MV-algebra $$A$$ there exists an extremal compact Hausdorff space $$M$$ and a regular representation $$\varphi:A \to A_1(M)$$.

##### MSC:
 06D35 MV-algebras 54C40 Algebraic properties of function spaces in general topology 54C30 Real-valued functions in general topology 54D30 Compactness 06F15 Ordered groups
##### Keywords:
MV-algebra; regular representation; Dedekind completion
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##### References:
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