论文标题
根本有限的环和空间曲线
Radically finite rings and space curves
论文作者
论文摘要
We define radically finite rings and show that finite dimensional radically finite rings are Noetherian, and that if either R is a finite character Hilbert domain that contains a field of characteristic zero or a finite dimensional Prufer domain, then the polynomial ring R[X] over R is radically finite if and only if R is a Dedekind domain with torsion ideal class group.然后，我们考虑UFD上的根本有限条件，并表明不存在Krull Dimension 2的有限字符UFD R，而多项式环R [X]在该r [x]上是从根本上有限的。因此，并非所有空间曲线都设置为理论完整交叉点。
We define radically finite rings and show that finite dimensional radically finite rings are Noetherian, and that if either R is a finite character Hilbert domain that contains a field of characteristic zero or a finite dimensional Prufer domain, then the polynomial ring R[X] over R is radically finite if and only if R is a Dedekind domain with torsion ideal class group. We then consider the radically finite condition on UFD and show that there does not exist a finite character UFD R of Krull dimension 2 over which the polynomial ring R[X] is radically finite. From this it follows that not all space curves are set theoretic complete intersection.
