Consider the sequence {0} ZZ6 Z3 {0} Z-modules Z2,Z3,Z6 and Z-module homomorphisms f and g, where f(m) = 3m for m Z and g(n) 2n mod 3 for n E Ze. Show that the sequence is a split exact sequence. = [20 marks] Let R be a ring. Let {0} MMM" {0} be an exact sequence of R-modules. Suppose M is noetherian. Show that M' and M" are also noetherian. [20 marks]