Abstract
Recently in Dvurecenskij and Zahiri (A variety containing EMV-algebras and Pierce sheaves, arXiv:1911.06625 ), new algebras called wEMV-algebras, which generalize MV-algebras, generalized Boolean algebras and EMV-algebras, were founded, and for these algebras a top element is not assumed a priori. For this class we define a state as a mapping from a wEMV-algebra into the real interval [0, 1] which preserves a kind of subtraction of two comparable elements and attaining the value 1 in some element. It can happen that some wEMV-algebras are stateless, e.g. cancellative ones. We characterize extremal states just as state-morphisms which are wEMV-homomorphisms from an algebra into the real interval [0, 1]. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal ideals having a special property. Moreover, we prove that under some conditions every state on a wEMV-algebra is a weak limit of a net of convex combinations of state-morphisms.
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