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Given an ample, Hausdorff groupoid $\mathcal{G}$, and a unital commutativering $R$, we consider the Steinberg algebra $A_R(\mathcal {G})$. First we provea uniqueness theorem for this algebra and then, when $\mathcal{G}$ is graded bya cocycle, we study graded ideals in $A_R(\mathcal {G})$. Applications aregiven for two classes of ample groupoids, namely those coming from actions ofgroups on graphs, and also to groupoids defined in terms of Boolean dynamicalsystems.

A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras