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To show a non-empty subset S of R is a subring if a,b∈S⇒a−b∈Sandab∈S
Clearly S is non-empty as 0 belongs to Ring R so, ax=0.
let x,y∈S⇒ ax=0,ay=0
is is needed to show that x−y∈S
Now show xy∈S
Therefore, S is a subring of ring R.
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