Sunday, October 30, 2016

abstract algebra - Right invertible and left zero divisor in matrix rings over a commutative ring


If a ring R is commutative, I don't understand why if A,BRn×n, AB=1 means that BA=1, i.e., Rn×n is Dedekind finite.




Arguing with determinant seems to be wrong, although det(AB)=det(BA)=1 but it necessarily doesn't mean that BA=1.




And is every left zero divisor also a right divisor ?



No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...