文献[1]热运用环论的方法证明了环Z[m~（1/2）]热的商环Z[m~（1/2）]/（a＋bm~（1/2））的元素个数是｜a2-b2m｜.我们将用主理想整环上的模的理论给出一种简洁的证明.%In [1], the author proved that the element number of the quoient ring Z [m]/（a ＋ b m） of integral domain Z [m] is ｜a^2 --b^2m｜ by the method of ring theory. We will give a concise proof on this result by the theory of modules over principal ideal domain.
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