Definition: If $xa+b=1$, there is a $y$ such that $a+yb$ is a unit

- A. A. Tuganbaev. Rings close to regular. (2013) @ Chapter 6
- T.-Y. Lam. A crash course on stable range, cancellation, substitution and exchange. (2004) @ .

- Morita invariant
- passes to matrix rings
- passes to $eRe$ for any full idempotent $e$
- stable under products
- stable under finite products

- passes to subrings (Counterexample: $R_{ 1 }$ is a subring of $R_{ 2 }$)
- passes to quotient rings (Counterexample: $R_{ 7 }$ is a homomorphic image of $R_{ 112 }$)

Rings

Legend

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