3
$\begingroup$

Is there any noncommutative ring without $1$ that has the following property?

Every right sided ideal is two sided too, but there exists a left sided ideal that is not two sided.

$\endgroup$
1
$\begingroup$

Take any right-not-left duo ring and take its product with a ring with a zero multiplication ring with $2$ elements.

The result is still right-not-left duo, but the zero ring ensures it does not have identity.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.