Talk:Noetherian module

I added a little bit about the history of the definition LkNsngth (talk) 06:05, 18 June 2008 (UTC)

Is the first bullet point in the section 'Characterizations, properties and examples' correct? It seems to me a counter-example to that statement is the set of submodules $2\mathbb {Z} ,3\mathbb {Z}$ of the $\mathbb {Z}$-module ${}_{\mathbb {Z} }\mathbb {Z}$, which has no maximal element. I can't see how the Axiom of Choice changes that.--Ajkirk (talk) 00:12, 11 November 2015 (UTC)

Aren't $2\mathbb {Z} ,3\mathbb {Z}$ both maximal elements of th set $\{2\mathbb {Z} ,3\mathbb {Z} \}$? (Maximal in the sense there is no other element properly containing it.) -- Taku (talk) 04:32, 11 November 2015 (UTC)

@Ajkirk Taku's comment is right. It looks a bit like you are thinking about a maximum element of a set rather than maximal elements. Could this be the case? Rschwieb (talk) 14:35, 11 November 2015 (UTC)