关于环Z[m~（1/2）]的商环元素个数的一个新的证明
관우배Z[m~（1/2）]적상배원소개수적일개신적증명
A New Proof on the Element Number of the Quotient Ring of the Ring Z[m]
  • 万方数据
    大学数学 대학수학
    COLLEGE MATHEMATICS
    2011年 5期 118-120 ,共3页

    张必成%赵巨涛

    장필성%조거도

    主理想整环%不变因子%素元%不可约元 主理想整環%不變因子%素元%不可約元
    주이상정배%불변인자%소원%불가약원
    principal ideal domain invarint factors%prime element%irreducible element
    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.
    문헌[1]열운용배론적방법증명료배Z[m~（1/2）]열적상배Z[m~（1/2）]/（a＋bm~（1/2））적원소개수시｜a2-b2m｜.아문장용주이상정배상적모적이론급출일충간길적증명.
    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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