(adsbygoogle = window.adsbygoogle || []).push({}); 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, 0_{R}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 0_{R}*0_{R}^{-1}is not an element of S. Hence S is not a subring of R, disproving the original claim.

I feel that the fact 0_{R}*0_{R}^{-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.

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# Subring: Prove or Disprove

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