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 $k\mathit{}\mathrm{Z}$.

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 $k\mathbb{Z}$
Canonical name	CyclicRingsThatAreIsomorphicToKmathbbZ
Date of creation	2013-03-22 16:02:42
Last modified on	2013-03-22 16:02:42
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	10
Author	Wkbj79 (1863)
Entry type	Corollary
Classification	msc 13A99
Classification	msc 16U99
Related topic	MathbbZ