Talk:Localization of a module

R-module or S^-1R-module?

I am not sure whether R-module (as in AtiyahEisenbud) or S^-1R-module (as in Atiyah) should be used in the definition of the localization of modules. --Kompik (talk) 12:41, 27 May 2008 (UTC)

The current article is fairly ambiguous about this. Both structures are extremely important, and there is a unique way to go from one to the other, so the current ambiguous approach might be best. JackSchmidt (talk) 13:38, 27 May 2008 (UTC)

Monomorphism?

What are necessary and sufficient conditions on M such that the homomorphism from M to S^-1M is one-one? Druiffic (talk) 16:12, 8 December 2008 (UTC)Druiffic

I'm not sure why this is showing up in code mode. :? --Druiffic (talk) 00:39, 9 December 2008 (UTC)Druiffic

(there was an initial space making it appear funnily)

If R is commutative, then it is necessary and sufficient that if s in S, m in M, and sm=0, then m=0. I think the same is true if S is an Ore set in general. This is often phrased as "S⁻¹ kills the S-torsion in M". The proofs could probably be done directly or by replacing R by its image in the endomorphism ring of the additive group of M. JackSchmidt (talk) 07:04, 20 December 2008 (UTC)

Article Merge

Perhaps this article could be combined with the article on the localization on the ring, after all, the two constructions are very related. LkNsngth (talk) 05:56, 4 February 2009 (UTC)

Against merger

The localisation of a module already uses the construction of localisation of a ring. To the best of my knowledge, it can not be defined standalone.--Mathmensch (talk) 13:55, 8 June 2016 (UTC) Or otherwise, we don't have a generalisation, as it's done in the article as I just saw.--Mathmensch (talk) 13:56, 8 June 2016 (UTC)