# Answer to Question #17366 in Algebra for Melvin Henriksen

Question #17366

Show that any unit-regular ring R is Dedekind-finite.

Expert's answer

Suppose

*ab*= 1*∈**R*, where*R*is unit-regular. Write*a*=*aua*, where*u**∈**U(**R*). Then 1 =*ab*=*auab*=*au*, so*a*=*u*^{−}^{1}*∈**U(**R*).
## Comments

## Leave a comment