Could You help me with this task?
"Proof that a commutative ring a is a local ring iff for any , from this that we have is an invertible element or is an invertible element."
Proof. - any element which satysfied equality and suppose that , where is a set of invertible elements of . We have then that . Since is an ideal, then also , and so . This is contradiction, so or .
- I'm not sure. Could You help me with this implication?