# Answer to Question #16896 in Abstract Algebra for Irvin

Question #16896

Show that for a semisimple module M over any ring R, the following conditions are equivalent:

(1) M is finitely generated;

(2) M is noetherian;

(3) M is artinian;

(4) M is a finite direct sum of simple modules.

(1) M is finitely generated;

(2) M is noetherian;

(3) M is artinian;

(4) M is a finite direct sum of simple modules.

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