Talk:Primary decomposition

message: If I'm not mistaken, the ideal (X_i^2\mid i\in\N)\subset k[X_i\mid i\in\N] has no primary decomposition because it has infinitely many associated primes, (X_i) for i\in\N.--gwaihir 23:28, 28 September 2006 (UTC)
thread_title:  Non-Noetherian rings? 

message: Tag this article as a 'technical article.'  —Preceding unsigned comment added by 71.111.251.229 (talk) 02:28, 15 December 2007 (UTC)
thread_title: Comment

message: The fundamental theorem of finitely generated Abelian groups is generalized by the modular extension of the Lasker–Noether theorem, not by the theorem itself, for Abelian groups are modules over Z.  —Preceding unsigned comment added by 85.146.200.37 (talk) 21:43, 20 May 2010 (UTC)
thread_title:  fundamental theorem of finitely generated abelian groups 

message: By this old edit,  credited Grete Hermann for the first primary decomposition algorithm. As far as I remember (I have not the article under hand), Hermann's article does not contains any such algorithm: its main focus is about linear algebra in polynomial rings (ideal membership, sygyzies, ...), and its consequences. Primary decomposition is not a direct consequence of linear algebra, partly because it requires factorization. Thus Hermann's article must be checked on this point. As far as I know, the first primary decomposition algorithm in polynomial rings over fields (for which pth roots are computable, where p is the characteristic) appears in Seidenberg's article Constructions in algebra (1974). For polynomial rings over the integers, an algorithm appears in another Seidenberg's article of the same year. D.Lazard (talk) 09:31, 3 June 2016 (UTC)
thread_title:  First primary decomposition algorithm 

message: :The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 
The result of the move request was: Not moved—a merge request is the right way to do this  buidhe 20:48, 2 May 2020 (UTC)
replies: text: Primary decomposition →  – In textbooks on commutative algebra, primary decomposition and associated primes are almost never discussed separately. Thus, maintaining separate articles for primary decomposition and associated primes is a bit weird. I suggest we move the article to this new name and move the materials in "associated prime" that concern the commutative case to this article. Taku (talk) 03:20, 25 April 2020 (UTC)

text: The discussion above is closed.  Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 I'm sorry for late response. I think we both agree that the current organization of the materials is not good; i.e., problematic emphasis on module or non-commutative cases. We disagree on specific resolutions to the problem. In any case, I have started the draft article Draft:Primary decomposition and associated prime which is meant to replace the current article as well as the commutative portion of associated prime. I have also begun implementing some of your suggestions like starting the article with the ideal case first. It is not finished but you can see the type of the article I have in mind. What do you think? -- Taku (talk) 05:35, 23 May 2020 (UTC)

text: Since the draft is now more or less ready to be published, if there is no objection from you or other editors, I am planning to replace the current article with the draft in the next few days. (No need to rush but also no need to wait if there is no issue). -- Taku (talk) 23:23, 26 May 2020 (UTC)

text: The new version has been published. —- Taku (talk) 23:35, 27 August 2020 (UTC)
thread_title:  Requested move 25 April 2020 

message: The redirect Coprimary 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  until a consensus is reached.  1234qwer1234qwer4 13:50, 7 May 2023 (UTC)
thread_title:  "[[:Coprimary]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]