2.3. If S be an ideal of a ring R and T be any subring of R, then S+T/S=~T/ S intersection T
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Answer:S is a subring of R if S is closed under subtraction and multiplication. Proof. We need to show S is closed under addition, has 0 and has additive inverses. But S = ∅ implies there is some s ∈ S, hence 0 = s − s ∈ S.
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