Global dimension of graded local rings

Let be a positively graded Noetherian ring. It is proved that if Ao/J(A0) is semisimple, where J(A0) is the Jacobson radical of A0, then gl. dimA = p. dimA(Ao/J(A0)). If A0, is a (not necessarily commutative) local ring with maximal ideal ω , then gl. dimA = p. dimA(A0/ω) = inj. dimA(A0/ω).