For abelian finitely generated semigroups, the reduced crossed product A ⋊_red P is exact if and only if A is exact, strengthening prior results by dropping the injective endomorphism hypothesis.
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Some remarks on Reduced $C^*$-algebras of semigroup dynamical systems and product systems
For abelian finitely generated semigroups, the reduced crossed product A ⋊_red P is exact if and only if A is exact, strengthening prior results by dropping the injective endomorphism hypothesis.