Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584535 | Journal of Algebra | 2014 | 16 Pages |
Abstract
Let R0 be a commutative and associative ring (not necessarily unital), G a group and α a partial action of G on ideals of R0, all of which have local units. We show that R0 is maximal commutative in the partial skew group ring R0âαG if and only if R0 has the ideal intersection property in R0âαG. From this we derive a criterion for simplicity of R0âαG in terms of maximal commutativity and G-simplicity of R0. We also provide two applications of our main results. First, we give a new proof of the simplicity criterion for Leavitt path algebras, as well as a new proof of the Cuntz-Krieger uniqueness theorem. Secondly, we study topological dynamics arising from partial actions on clopen subsets of a compact set.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniel Gonçalves, Johan Ãinert, Danilo Royer,