A NOTE ON THE JACOBSON RADICAL OF A GRADED

Abstract. We prove that J(Re) = Re∩J(R), where S is a cancellative partial groupoid with idempotent e, R = s∈S Rs an Artinian S-graded ring inducing S, J(R) the Jacobson radical of R and J(Re) the Jacobson radical of Re. We also prove that J(R) is nil if J(Re) is nil under certain assumptions