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Keywords:
$MV$-algebra; archimedean $MV$-algebra; completeness; singular $MV$-algebra; higher degrees of distributivity
$MV$-algebra; archimedean $MV$-algebra; completeness; singular $MV$-algebra; higher degrees of distributivity
Summary:
In this paper we deal with the of an $MV$-algebra $\mathcal A$, where $\alpha $ and $\beta $ are nonzero cardinals. It is proved that if $\mathcal A$ is singular and $(\alpha,2)$-distributive, then it is . We show that if $\mathcal A$ is complete then it can be represented as a direct product of $MV$-algebras which are homogeneous with respect to higher degrees of distributivity.
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