The prime ideals of a polynomial ideal under extension of the base field
The prime ideals of a polynomial ideal under extension of the base field
复制标题
基域扩张下多项式理想的素理想
DOI：
--
复制
发表时间：
1975
期刊：
影响因子：
--
通讯作者：
A. Seidenberg
中科院分区：
文献类型：
--
作者：
A. Seidenberg
设k是域，k′是代数扩张域，X1，…，Xn不定，A是k[X1，...，Xn]，且令A′ = k[X1，...，Xn]A.证明了A′的任何相伴素数在k[X1，...，[1] A的一个相关素数。Krull的其他一些老问题也得到了回答。
SummaryLet k be a field, k′ an algebraic extension field, X1, ..., Xn indeterminates, A an ideal in k[X1, ..., Xn], and let A′ = k[X1, ..., Xn]A. It is shown that any associated prime of A′ contracts in k[X1, ..., Xn] to an associated prime of A. Some other old questions of Krull are also answered.