1. The problem statement, all variables and given/known data Prove or Disprove: The set of units in a ring R with identiy is a subring of R. 2. Relevant equations 3. The attempt at a solution Let S be the the set of units in a ring R with identity. For S to be a subring of R, 0R would have to be an element of S. Since S is the set of units in R, it follows that S will not a multiplicative identity, namely 0R*0R-1 is not an element of S. Hence S is not a subring of R, disproving the original claim. I feel that the fact 0R*0R-1 is not an element of S is the main part of the proof. I am just unsure if my argument and logic are correct.