Talk:Isomorphism theorems

message: Following herstein, I'm not familiar with the concept of the "image of a mapping" as used in
the statement of the first theorem. a mapping has a range (or codomain), and any subset of it's
domain has an image under the mapping. But the "image of a mapping" is a concept I've not encountered.
If I interpret "image of a mapping" to mean it's codomain, then the 3rd list item
is restating the conclusion of the "in particular" qualification that immediately follows, 
only it omits the requirement for the mapping to be surjective -- which makes it wrong.  — Preceding unsigned comment added by 5.102.207.31 (talk) 03:03, 7 April 2014 (UTC)
replies: text: The image of the map is the image of the domain under the map. Magidin (talk) 16:42, 7 April 2014 (UTC)
thread_title:  The first theorem 

message: Editor Sbilley made edits adding Noether's name to most references to the isomorphism theorems. The edit summary says that the editor "was tasked" with updating the name; tasked by whom, exactly? Has this been discussed and consensus reached? Further, the proffered justification for the changes  is that in Math "it is typical to attribute theorems to the original author". Things are called what they are called, not what they ought to be called (Quadratic Reciprocity is called "Quadratic Reciprocity", not "Gauss's Law of Quadratic Reciprocity", for example).  I am not familiar with any standard reference to the isomorphism theorems that calls them "Noether's Isomorphism Theorems". Even if the attribution is accurate, if the theorems are not called that in the literature, then they should not be called that in the article; an attribution is certainly in order, or even a brief mention in the lede, but it seems to me that the kind of wholesale re-branding that this editor is doing here is ill-advised at best, and in any case needs consensus. Magidin (talk) 22:08, 27 October 2016 (UTC)
replies: text: Thank  you for the response. I take the introduction to mean that you were not so much "tasked", as that you decided to take it upon yourself, inspired perhaps by the talk in question. As such, I would say that this needs to be discussed, probably at the Wikipedia talk:WikiProject Mathematics page, rather than simply done. If adopted, this would require a lot more changes than just in this page. I will also note that the talk said we should be using the name, not that we do; the page should reflect common usage. I'm at home, but I will look up in my bookshelf to provide specific instances. I think that the name "Noether's Isomorphism Theorems" is simply not widespread enough to warrant the kind of wholesale change you made. I support adding attribution, and perhaps even a section on the name, but this is a sort of advocacy-through-naming-in-Wikipedia that does not seem warranted. We can take it to the WikiProject, if you wish, given the low traffic here, before determining what the consensus is. Magidin (talk) 21:12, 29 October 2016 (UTC)
replies: text:  Here's from my bookshelf: Groups and Symmetry by M.A. Amstrong; "Isomorphism Theorems". Representation Theory of Finite Groups and Associative Algebras by Curtis and Reiner; "Fundamental Theorem on Homomorphisms". Abstract Algebra, by Dummit and Foote; "Isomorphism Theorems". Basic Algebra by Jacobson; "Fundamental Theorem of Homomorphisms of Monoids and Groups". Algebra by Thomas Hungerford; "Isomorphism Theorems". A course in Group Theory by John Humphreys; "Homomorphism Theorem". Universal Algebra by Grätzer; "Isomorphism Theorems". Algebra by Serge Lang; no name given. Groups and Geometry by Peter Neumann, Gabrielle Stoy, and Edward Thompson; "Isomorphism Theorems". An introduction to the theory of groups (4th Ed) by Joseph Rotman; "Isomorphism Theorems". A course in the theory of groups (2nd ed) by Derek Robinson; "Isomorphism Theorems". Advanced Modern Algebra (2nd ed) by Joseph Rotman; "Isomorphism Theorems". Elements of Algebra by John Stillwell; "Isomorphism theorem for groups". None of my books refer to them "Soether Isomorphism Theorems". Magidin (talk) 16:37, 3 November 2016 (UTC)
replies: text:    You're wrong about Robinson, look at the name of the section. Njsnyder (talk) 16:59, 31 October 2017 (UTC)
thread_title:  Noether's Isomorphism Theorems 

message: In the second isomorphism theorem, it says that  [B]^{\Phi} is the collection of equivalence classes but what follows has no sense. It should probably be
:  [B]^{\Phi}=\left\lbrace K\in A \mid \exists\, b\in B,\; \Phi \cap (K,b) \neq \emptyset \right\rbrace / \Phi 
Noix07 (talk) 16:22, 17 October 2018 (UTC)
replies: text:  Ah, now I get it, i previously thought the slash meant "so that". K \in (A/ \Phi) so that... Noix07 (talk) 16:29, 17 October 2018 (UTC)
thread_title: General case