| A commutative ring R is said to be Chinese if, given a, b 6 R and ideals A, B of R such that a ≡ b(A + B), there exists c ∈ R such that c ≡ a(A) and c ≡ b(B). Chinese rings were investigated by K.E.Aubert and I.Beck in 1982. However, in their paper, they said that they were unable to settle the case whether the ring Z[X] is Chinese or not. In this paper, we provide a short proof to show that the ring Z[X] is not Chinese. The techinque we used here is different from Aubert and Beck. Moreover, we show that for any algebraic numbers α1,…,αn, the ring Z|α1,…,αn|is Chinese for n≥1. |
