When is a subgroup of a ring an ideal? (Q292495)

Let \(R\) be a commutative ring and the authors study when a subgroup of \((R,+)\) is an ideal of \(R\). For cases \(\mathbb Z\times \mathbb Z\) and \(\mathbb Z_n\times \mathbb Z_m\), where \(n,m\in \mathbb N\), computable criterions are given (see Proposition 3.1, Theorem 3.8, Theorem 4.1, and Theorem 4.6). The authors also obtain the probability of a randomly chosen subgroup in \(\mathbb Z_n\times \mathbb Z_m\) is an ideal (see Theorem 5.4).