# Who defined and who coined “module”?

The title of my Q. says it all:

QUESTION:   Who defined and who coined: module?

Would it be Emmy Noether?

EDIT   In view of @anon's and KConrad's answers, and as it could have been expected, the situation is a bit complex. Thus it looks that while Dedekind coined module, the final notion was defined by Emmy Noether. By defined I mean that module at a minimum should be a generalization of linear spaces, abelian groups and ideals.

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I would say, in answer to your edit, that if that is your definition of "define" then Dedekind both coined and defined the term (just like he coined the term "ideal", as opposed to "ideal number"). Noether generalized, just like she generalized a lot of the theory of rings and ideals, but according to Stillwell in the work quoted by anon, she was fond of saying "Es steht schon bei Dedekind" ("It is already in Dedekind") when talking about ideals/modules. – Arturo Magidin Aug 23 '14 at 2:08

This is right: it goes back to Dedekind's work, although he didn't have the concept as abstract as Emmy Noether did later on. For Dedekind, the concept was what we'd call a (finite free) $\mathbf Z$-module. Another reference mentioning this is in volume 2 of Ewald's "From Kant to Hilbert", where the relevant part can be seen at books.google.com/… – KConrad Aug 22 '14 at 23:39