Exercise 4, § 8

Let A be a pseudo-ring in which every additive subgroup of A is a left ideal of A.

(a) If A is a ring, A is canonically isomorphic to $\mathbf{Z}/n\mathbf{Z}$ for some suitable integer $n$.

(b) If A has no unit element and every non-zero element is cancellable, A is isomorphic to a pseudo-subring of $\mathbf{Z}$.