论文标题
计算支持的关闭
Computing the closure of a support
论文作者
论文摘要
当$ e $是$ r $ - 模块上的$ r $ module时，zariski的支撑封口是$ \ mathrm v（\ mathcal o（e））$的形式，其中$ \ mathcal o（e）$是独特的自由基理想。我们给出了$ \ Mathcal o（e）$的明确形式，并在代数的各种操作下研究其行为。给出了应用程序，特别是用于关闭支撑的换向Unital环的环。我们为环形扩展的关键和关键理想提供了一些应用。
When $E$ is an $R$-module over a commutative unital ring $R$, the Zariski closure of its support is of the form $\mathrm V(\mathcal O(E))$ where $\mathcal O(E)$ is a unique radical ideal. We give an explicit form of $\mathcal O(E)$ and study its behavior under various operations of algebra. Applications are given, in particular for ring extensions of commutative unital rings whose supports are closed. We provide some applications to crucial and critical ideals of ring extensions.
