Definition: (Invariant Basis Number) If $R^n$ is isomorphic to $R^m$, then $n=m$

- T.-Y. Lam. Lectures on modules and rings. (2012) @ Chapter 1, Section 1

- passes to subrings
- stable under products
- stable under finite products
- passes to the center

- passes to quotient rings (Counterexample: $R_{ 79 }$ is a homomorphic image of $R_{ 166 }$)
- Morita invariant (Counterexample: $R_{ 171 }$ is Morita equivalent to $R_{ 172 }$)

Rings

Legend

- = has the property
- = does not have the property
- = information not in database