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On intervals and the dual of a pseudo MV-algebra. (English) Zbl 1150.06013
Pseudo MV-algebras are a non-commutative generalization of MV-algebras. A. Dvurečenskij proved that every pseudo MV-algebra $$\mathcal A$$ is isomorphic to an interval $$[o,u]$$ of an $$\ell$$-group $$G$$ with a strong unit $$u$$. In this paper, Dvurečenskij’s result is used in order to define the pseudo MV-algebra dual of $$\mathcal A$$, $$\mathcal A^{\text{dual}}$$. In the framework of this dual construction, the systems of intervals, as well as the interval direct product decompositions of pseudo MV-algebras are investigated.

##### MSC:
 06D35 MV-algebras
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##### References:
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