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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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