Hi, let me just say that I'm not in a class or anything, I'm just working through an old book and trying to understand.

Problem: Give an example of a ring with unity 1 that has a subring with unity $\displaystyle 1' \not= 1$.

So my ring must be not commutative or be such that not every nonzero element has a multiplicative inverse, since in a field "the unity element of a subfield must be the unity of the whole field." But I can't find an example. Thanks in advance!