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Radicals in non-commutative generalizations of MV-algebras. (English) Zbl 1008.06011
GMV-algebras (or pseudo MV-algebras) are noncommutative generalizations of Chang’s MV-algebras. Recently, A. Dvurečenskij proved that the category of GMV-algebras is equivalent to the category of \(\ell \)-groups with strong unit.
This categorical equivalence is used by the author in order to study three kinds of radicals of an GMV-algebra. Several characterizations of finite-valued GMV-algebras are obtained.
It is shown that a normal-valued and not completely distributive GMV-algebra has infinitely many state-morphisms.

MSC:
06D35 MV-algebras
06F15 Ordered groups
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