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

###### Corollary.

An infinite cyclic ring (http://planetmath.org/CyclicRing3) with positive behavior $k$ is isomorphic to $k\mathbb{Z}$.

###### Proof.

Note that $k\mathbb{Z}$ is an and that $k$ is a generator (http://planetmath.org/Generator) of its additive group. Since $k^{2}=k(k)$, then $k\mathbb{Z}$ has behavior $k$. ∎

Title cyclic rings that are isomorphic to $k\mathbb{Z}$ CyclicRingsThatAreIsomorphicToKmathbbZ 2013-03-22 16:02:42 2013-03-22 16:02:42 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Corollary msc 13A99 msc 16U99 MathbbZ