多项式环的算术性质

The Arithmetic Property of Polynomial Rings

通过对整系数多项式环的由二次首一整系数不可约多项式生成的理想的研究,找出系数的关系使得相应的剩余类环为惟一分解环,或者是主理想整环,或者是欧氏整环的条件。由此可得到一些是主理想整环但不是欧氏整环的例子。

Based on the ideal research on integral coefficient polynomial rings generated by irreducible quadratic with first coefficient one integral coefficient polynomials, the coefficient relationship is determined so that the corresponding surplus ring becomes the condition for the unique factorization domain, the Euclidean ring. Hence, examples of principal ideal domain not Euclidean domain are obtained.