Abstract
Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state.
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Dvurečenskij, A. States on Pseudo MV-Algebras. Studia Logica 68, 301–327 (2001). https://doi.org/10.1023/A:1012490620450
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DOI: https://doi.org/10.1023/A:1012490620450