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In this paper we give some sufficient and some necessary conditions for an\'etale groupoid algebra to be a prime ring. As an application we recover theknown primeness results for inverse semigroup algebras and Leavitt pathalgebras. It turns out that primeness of the algebra is connected with thedynamical property of topological transitivity of the groupoid. We obtainanalogous results for semiprimeness.

Prime \'etale groupoid algebras with applications to inverse semigroup and Leavitt path algebras