Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicity of skew inverse semigroup rings with applications to
  Steinberg algebras and topological dynamics   Given a partial action $\pi$ of an inverse semigroup $S$ on a ring
$\mathcal{A}$ one may construct its associated skew inverse semigroup ring
$\mathcal{A} \rtimes_\pi S$. Our main result asserts that, when $\mathcal{A}$
is commutative, the ring $\mathcal{A} \rtimes_\pi S$ is simple if, and only if,
$\mathcal{A}$ is a maximal commutative subring of $\mathcal{A} \rtimes_\pi S$
and $\mathcal{A}$ is $S$-simple. We apply this result in the context of
topological inverse semigroup actions to connect simplicity of the associated
skew inverse semigroup ring with topological properties of the action.
Furthermore, we use our result to present a new proof of the simplicity
criterion for a Steinberg algebra $A_R(\mathcal{G})$ associated with a
Hausdorff and ample groupoid $\mathcal{G}$.

24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph