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# cyclic rings that are isomorphic to $k\mathbb{Z}$

###### Corollary.

An infinite cyclic ring with positive behavior $k$ is isomorphic to $k\mathbb{Z}$.

###### Proof.

Note that $k\mathbb{Z}$ is an infinite cyclic ring and that $k$ is a generator of its additive group. Since $k^{2}=k(k)$, then $k\mathbb{Z}$ has behavior $k$. ∎

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## Mathematics Subject Classification

13A99*no label found*16U99

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