## Stream: maths

### Topic: notation for finite free modules

#### Kevin Buzzard (Aug 22 2018 at 10:29):

Some students here have developed the basic theory of free modules of finite rank over a ring (which later becomes a commutative ring and then a field). One issue I have with their work is that they are still using some placeholder notation for the fundamental construction of $R^n$, the free rank $n$ module over the ring $R$. What should the function which takes a ring R and a natural n and returns the R-module R^n be called? Any suggestions?

#### Reid Barton (Aug 22 2018 at 14:19):

I guess there are two questions: name, and notation

#### Reid Barton (Aug 22 2018 at 14:20):

For notation, assuming we can't use R^n, how about R^⊕n?

#### Johan Commelin (Aug 22 2018 at 14:25):

Why can't we use R^n? As for the name, how about finite_free_module R n?

#### Reid Barton (Aug 22 2018 at 14:34):

Maybe we can use R^n, but in that case I assumed there was no choice to be made :)

Last updated: May 18 2021 at 08:14 UTC