Question

Give an example, with justification ,, of a subset of a ring that is a subgroup under addition but not a subring

Answer 1

Answer:

Let R = C and S = {ix : x ∈ R}. Then 0 ∈ S and a − b ∈ S

whenever a, b ∈ S. But i · i = −1 ∈/ S.

Step-by-step explanation:

Let R = C and S = {ix : x ∈ R}.

Then 0 ∈ S and

a − b ∈ S

so subset of a ring that is subgroup under addition

whenever a, b ∈ S.

But i · i = −1 ∈/ S.

but not a subring