  Let $R$ be a unital commutative ring with unit and $\mathscr{G}$ an ample
groupoid. Using the topology of the groupoid $\mathscr{G}$, Steinberg defined
an etale groupoid algebra $R\mathscr{G}$. These etale groupoid algebras
generalize various algebras including group algebras, commutative algebras over
a field generated by idempotents, traditional groupoid algebras, Leavitt path
algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg
later characterized the classical chain conditions for etale groupoid algebras.
We characterize categorically noetherian and artinian, locally noetherian and
artinian, and semisimple etale groupoid algebras, generalizing existing results
for Leavitt path algebras.
