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State morphism MV-algebras
We present a complete characterization of subdirectly irreducible MV-algebras
with internal states (SMV-algebras). This allows us to classify subdirectly
irreducible state morphism MV-algebras (SMMV-algebras) and describe single
generators of the variety of SMMV-algebras, and show that we have a continuum
of varieties of SMMV-algebras
Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State
Recently Flaminio and Montagna, \cite{FlMo}, extended the language of
MV-algebras by adding a unary operation, called a state-operator. This notion
is introduced here also for effect algebras. Having it, we generalize the
Loomis--Sikorski Theorem for monotone -complete effect algebras with
internal state. In addition, we show that the category of divisible
state-morphism effect algebras satisfying (RDP) and countable interpolation
with an order determining system of states is dual to the category of Bauer
simplices such that is an F-space
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