# Example of a noncommutative, nonunital ring with this property about its ideals?

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.

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.