Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State

Abstract

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 $\sigma$-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 $\Omega$ such that ${\partial }_e\Omega$ is an F-space.

References in corpus (1)

• Stone Duality Type Theorems for MV-algebras with Internal State

Cited by in corpus (1)

• The Lattice and Simplex Structure of States on Pseudo Effect Algebras