Definition talk:Dimension of Module

Did we really have to change this to "Dimension of Free Module" after all?

This was originally defined as "Dimension of Module", and defined on a unitary module which has $n$ elements in its basis.

Hence you can't have a dimension of a module which is not free.

Hence you don't need to include "free" in the title, and just by declaring that your module has a dimension indicates that it has to be free.

Unless we can find a definition of the dimension of a module which is not free, I contend there's no point in renaming everything to include "free" in it.

I should have noticed this last night but I'd been out. --prime mover (talk) 05:04, 9 August 2023 (UTC)

First, I strongly doubt the validity of this definition of dimension of (free) module. Is the cardinality of the base really unique? I could not find any source for this definition. Second, I was about to introduce the (Krull) dimension of modules. This is just an algebraic one, and has nothing to do with the dimension of vector space. So, I will name the latter Krull dimension. --Usagiop (talk) 15:14, 9 August 2023 (UTC)

It seems OK, Bases of Free Module have Equal Cardinality. --Usagiop (talk) 15:17, 9 August 2023 (UTC)