Separability for relative extensions of object unital strongly groupoid graded rings

Zaqueu Cristiano, Patrik Lundström

We prove that if $R$ is a ring that is object unital and strongly graded by a groupoid $\Gamma$, and if $\Delta$ is a wide subgroupoid of $\Gamma$, then $R/R_{\Delta }$ is separable if and only if, for e…