Pairs of domains where all intermediate domains are Noetherian
Pairs of domains where all intermediate domains are Noetherian
复制标题
所有中间域都是诺特域的域对
DOI：
10.1090/s0002-9947-1974-0349665-2
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发表时间：
1974
影响因子：
1.3
通讯作者：
A. Wadsworth
中科院分区：
文献类型：
--
作者：
A. Wadsworth
.对于R和T的诺特整域R和T，若R，T是诺特整域，则称（R，T）为诺特对（NP）.当dim R - 1（Krull维数），它表明，唯一的NP的是那些由Krull-Akizuki定理。对于dim R a 2，除了有限积分扩张外，还存在另一种NP，即（/？n）其中ft =1 li/？„| rk P a 2（.此外，对于每个NP（p，T）且dim <$2，则存在R的整数NP扩张B，其中Tc B。在所有已知的例子中，B可以被选择为R的有限积分扩张。对于这样的NP's，证明了NP关系是传递的。T本身可以是一个无限的整数扩张R，虽然，并给出了一个例子。不知道哪些无限积分扩张是NP的。
. For Noetherian integral domains R and T with R S T, (R, T) is called a Noetherian pair (NP) if every domain A, R Q A Q T, is Noetherian. When dim R - 1 (Krull dimension) it is shown that the only NP's are those given by the Krull-Akizuki Theorem. For dim R a 2, there is another type of NP besides the finite integral extension, namely (/?, n) where ft =1 li/?„|rk P a 2(. Further, for every NP (/?, T) with dim Ä i2 there is an integral NP extension B of R with T c B. In all known examples B can be chosen to be a finite integral extension of R. For such NP's it is shown that the NP relation is transitive. T may itself be an infinite integral extension R, though, and an example of this is given. It is unknown exactly which infinite integral extensions are NP's.