Well, I have another question.
Suppose A is a ring with unity denoted by 1. Let S be the set of elements in A that have multiplicative inverses in A.
I want to prove S is a group under mult. I know the four cases that must be proved. However, I'm having a little difficulty as to how I should prove that these particular things are in the set of elements S.
For example, the last case is to prove that for every element in S there is a multiplicative inverse. However, I am having a hard time thinking as to how I should prove the the inverses reside in S.
If this is vague, I am more than happy to explain what I mean.