Bourbaki

Exercise 1, § 2

Tag 002L, permanent. Cite it as [Bourbaki, Tag 002L].

Algebra, VIII, p. 39

a) Give an example of a Noetherian module M such that every nonzero endomorphism of M is injective and that there exist nonzero nonbijective endomorphisms of M.

b) Give an example of an Artinian module M such that every nonzero endomorphism of M is surjective and that there exist nonzero nonbijective endomorphisms of M.

Solution

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Transcribed from the printed volume. Not translated.