0

Does anyone have examples in mind that following statements are true for vector spaces over a division ring, but need not be true for modules over an arbitrary ring?

Every maximal linear independent set in a free module is a basis.

Every minimal spanning set in a free module is a basis.

Every quotient of a free module is free.

Community
  • 1
  • What do you mean by basis? the usual definitions go crazy quite fast! and for the last one: $\mathbb{Z}/n \mathbb{Z}$ for $n > 1$. – Felix Nov 18 '19 at 15:18
  • The last one is weird, considering vector spaces. All modules over division rings are free. – rschwieb Nov 18 '19 at 15:27

0 Answers0