Blog 1

Random Talk on Random Thoughts

Subring of Ring With Unity

| Comments |

I’ve just read a statement which asserts that a subring isomorphic to $\Z$ or $\Z_n$ can be found in any ring $R$ with unity. The proof which is based on a ring homomorphism $\phi:\Z\to R$ defined by $\phi(m) = m\cdot 1$ isn’t difficult to read.

I used fifteen minutes to think of why one needs a subring inside the ring $R$ with unity, instead of $R$. After I’ve come up with $R=\langle1,\frac{1}{2}\rangle=\left\{\frac{a}{2^b} \,\middle|\, a \in \Z, b \in\Z_{\ge 0} \right\}$, I start this post.