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.
2026-04-05 21:48:04.1775425684
Example of a noncommutative, nonunital ring with this property about its ideals?
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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.