On partial Galois Azumaya extensions

Let $\alpha$ be a globalizable partial action of a finite group $G$ over a unital ring $R$, $A=R\star_\alpha G$ the corresponding partial skew group ring, $R^\alpha$ the subring of the $\alpha$-invariant elements of $R$ and $\alpha^\star$ the partial inner action of $G$ (induced by $\alpha$) on the centralizer $C_A(R)$ of $R$ in $A$. In this paper we present equivalent conditions to characterize $R$ as an $\alpha$-partial Galois Azumaya extension of $R^\alpha$ and $C_A(R)$ as an $\alpha^\star$-partial Galois extension of the center $C(A)$ of $A$. In particular, we extend to the setting of partial group actions similar results due to R. Alfaro and G. Szeto [1, 2, 3].