Question: Consider the ring (Z3, , ) where addition and multiplication are defined by (a, b, c) (d, e, f) = (a + d, b

Consider the ring (Z3, ⊕, ⊙) where addition and multiplication are defined by (a, b, c) ⊕ (d, e, f) = (a + d, b + e, c + f) and (a, b, c) ⊙ (d, e, f) = (ad, be, cf). (Here, forex- ample, a + d and ad are computed by using the standard binary operations of addition and multiplication in Z.) Let S be the subset of Z3 where S = {(a, b, c)\a = b + c}. Prove that S is not a subring of (Z3, ⊕, ⊙).

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