1

I was reading this question.

I understand Alex's answer using tensor products except the last part. I guess his conclusion is if $F^n \simeq F^m$ have the same module structure then $n=m$, but I don't know why this is true. Can anyone elaborate on this?

Jason Dil
  • 315
  • 1
    The question you've linked to is far more general than the one you posed, and the answer you've referred to basically reduces the general case down to the field case, i.e. your question. The field case is proven with garden variety finite dimensional linear algebra. – Theo Bendit Oct 21 '19 at 04:51

1 Answers1

2

Note that a module over a field is a vector space. So, Alex's answer is referring to the dimension theorem for vector spaces.

Ben Grossmann
  • 225,327