Stably finite ring

In mathematics, particularly in abstract algebra, a ring R is said to be stably finite (or weakly finite) if, for all square matrices A and B of the same size with entries in R, AB = 1 implies BA = 1.

Namely, any nontrivial[notes 1] stably finite ring has IBN.

Subrings of stably finite rings and matrix rings over stably finite rings are stably finite.

A ring satisfying Klein's nilpotence condition is stably finite.

This abstract algebra-related article is a stub.