Talk:Commutative ring

nonrecursive definition

the current definition depends on the definition of a ring, and it would make sense to have a standalone definition on this page. Pdbailey (talk) 02:06, 30 May 2008 (UTC)[reply]

Having reread the definition of ring (mathematics), I withdraw this suggestion. Pdbailey (talk) 19:47, 30 May 2008 (UTC)[reply]

I agree with this. It is very helpful to have the full definition here, so I have added it. Depassp (talk) 05:39, 14 November 2008 (UTC)[reply]

I'm not convinced it is better to have the full definition here. For example abelian group doesn't redefine what a group is; it seems redundant to repeat seven of the axioms of a ring and add an eighth. As the article currently stands, one would have to look closely at all the axioms to ensure that in fact the only difference between this definition and that of a ring is that a.b=b.a. It seems more natural to not repeat the full definition of a ring here. Mlm42 (talk) 07:59, 16 November 2008 (UTC)[reply]

More examples?

The article Product (mathematics) has a section listing 3 rather basic commutative rings that college students might encounter. Those examples really kind-of don't belong there, cause they don't really have much to do with products per-se other than that rings have a product. However, this article is completely missing any section of "basic examples of commutative rings that beginner students might bump into" -- could that section be moved to here? Anyone? 67.198.37.16 (talk) 21:53, 4 September 2015 (UTC)[reply]

Rank of a free module

I understand and support the warning that modules are much more complicated than vector spaces. However, saying that even the rank of a free module may not be uniquely defined is confusing in an article about commutative rings. One might either remove the sentence or turn it into something like "However, in contrast with the situation over non-commutative rings, at least every free module has a uniquely defined rank, see (link to the wiki-page about invariant basis number)." Cheeseruch (talk) 18:33, 10 June 2022 (UTC)[reply]

Good point. However, the rank of a free module is a minor aspect of module theory. Therefore I have removed this sentence, and replaced it with the mention of modules of finite type, which are central to the theory. D.Lazard (talk) 09:16, 11 June 2022 (UTC)[reply]

"Cring" listed at Redirects for discussion

The redirect Cring has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 March 26 § Cring until a consensus is reached. 1234qwer 1234qwer 4 01:26, 26 March 2024 (UTC)[reply]