Abstract
We enlarge the class of C⁎-algebras of Boolean dynamical systems in order to include all weakly left-resolving normal labelled space C⁎-algebras in it. We prove a gauge-invariant uniqueness theorem and classify all gauge-invariant ideals of these C⁎-algebras of generalized Boolean dynamical systems and describe the corresponding quotients as C⁎-algebras of relative generalized Boolean dynamical systems.
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