The ideal structure of partial skew groupoid rings with applications to topological dynamics and ultragraph algebras

Under the hypotheses D_g s-unital for all g and R = ⊕_{e∈G_0} D_e, the paper proves a bijection between G-invariant ideals of R and G-graded ideals of R⋊_α G (Theorem 3.10), constructed via Ψ(J) = ⊕_g (J∩D_g)δ_g and Φ_gr(I) = P_0(I). The candidate solution reconstructs the same correspondence and uses the same s-unit techniques to show G-invariance, ideal closure, and mutual inverses, mirroring Propositions 3.8–3.9 and the proof of Theorem 3.10 in the paper. No missing hypotheses or logical gaps were found, and the steps align closely with the paper’s arguments .