Abstract
We show that every linear pseudo BL-algebra, hence every representable one, admits a state and is good. This solves positively the problem on the existence of states raised in Dvurecenskij and Rachůnek (Probabilistic averaging in bounded communitative residuated l-monoids, 2006), and gives a partial answer to the problem on good pseudo BL-algebras from [Di Nola, Georgescu and Iorgulescu (Multiple Val Logic 8:715–750, 2002) Problem 3.21]. Moreover, we present that every saturated linear pseudo BL-algebra can be expressed as an ordinal sum of Hajek’s type of irreducible pseudo linear pseudo BL-algebras.
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