direct product of noetherian submodlulea is again noetherian.(part a)

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(part b)direct product of noetherian modules is noetherian and sum of noetherian sub.is noetherian. (part b)direct product of noetherian modules is noetherian and sum of noetherian sub.is noetherian.
Finite Products of Noetherian Modules are Noetherian Finite Products of Noetherian Modules are Noetherian
Modules (Part 2, Herstein) Modules (Part 2, Herstein)
if submodule and quotient module of M is artinian then so is M. (part a) if submodule and quotient module of M is artinian then so is M. (part a)