(a) If M is a left algebra A-module, then (M) = {r A I rc =...

(a) If M is a left algebra A-module, then α(M) = {r ϵ A I rc = 0 for all c ϵ M} is an algebra ideal of A.

(b) An algebra ideal P of A is said to be primitive if the quotient algebra R/P is primitive (that is, has a faithful simple algebra R/P-module). Show that every primitive algebra ideal is a primitive ideal of the ring A and vice versa.