A Note on the Jacobson Radical of a Graded Ring - Ilić-Georgijević, Emil (Sarajevo Journal of Mathematics, 2024)
We prove that J(R_e)=R_eJ(R), where S is a cancellative partial groupoid with idempotent e, R=_sSR_s an Artinian S-graded ring inducing S, J(R) the Jacobson radical of R and J(R_e) the Jacobson radical of R_e. We also prove that J(R) is nil if J(R_e) is nil under certain assumptions.