Talk:Associated prime: Difference between revisions

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Is this commutative wikipedia? If not, I wonder why this article discusses associated primes only in the commutative setting. Liransh Talk 17:17, 4 March 2009 (UTC)[reply]

I am vastly amused by this specificity of this complaint. DS (talk) 15:02, 3 April 2009 (UTC)[reply]

Also, the article mentions that in the commutative setting, they are linked to Noether-Lasker decomposition. I think this is a little bit narrow. It is true that the associated primes are the radicals of Noether-Lasker components, but it is also true that given any finite irreducible decomposition in any commutative ring, the radicals of the components are the associated primes. The existence theorem requires Noetherianness, but the uniqueness claims of the Noether-Lasker theorem are much more general. 71.227.119.236 (talk) 17:34, 8 December 2012 (UTC)[reply]

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	:I am vastly amused by this specificity of this complaint. [[User:DragonflySixtyseven\|DS]] ([[User talk:DragonflySixtyseven\|talk]]) 15:02, 3 April 2009 (UTC)		:I am vastly amused by this specificity of this complaint. [[User:DragonflySixtyseven\|DS]] ([[User talk:DragonflySixtyseven\|talk]]) 15:02, 3 April 2009 (UTC)

			Also, the article mentions that in the commutative setting, they are linked to Noether-Lasker decomposition. I think this is a little bit narrow. It is true that the associated primes are the radicals of Noether-Lasker components, but it is also true that given any finite irreducible decomposition in any commutative ring, the radicals of the components are the associated primes. The existence theorem requires Noetherianness, but the uniqueness claims of the Noether-Lasker theorem are much more general. [[Special:Contributions/71.227.119.236\|71.227.119.236]] ([[User talk:71.227.119.236\|talk]]) 17:34, 8 December 2012 (UTC)