proof that every subring of a cyclic ring is a cyclic ring
(Proof)
The following is a proof that every subring of a cyclic ring is a cyclic ring.
Proof. Let $R$ be a cyclic ring and $S$ be a subring of $R$ Then the additive group of $S$ is a subgroup of the additive group of $R$ By definition of cyclic group, the additive group of $R$ is cyclic. Thus, the additive group of $S$ is cyclic. It follows that $S$ is a cyclic ring.
"proof that every subring of a cyclic ring is a cyclic ring" is owned by Wkbj79.
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