CHAIN CONDITIONS ON ÉTALE GROUPOID ALGEBRAS WITH APPLICATIONS TO LEAVITT PATH ALGEBRAS AND INVERSE SEMIGROUP ALGEBRAS

The author has previously associated to each commutative ring with unit R and etale groupoid G with locally compact, Hausdorff and totally disconnected unit space an R-algebra RG. In this paper we characterize when RG is Noetherian and when it is Artinian. As corollaries, we extend the characterization of Abrams, Aranda Pino and Siles Molina of finite-dimensional and of Noethenan Leavitt path algebras over a field to arbitrary commutative coefficient rings and we recover the characterization of Okninski of Noetherian inverse semigroup algebras and of Zelmanov of Artinian inverse semigroup algebras.