论文标题
OHM-RUSH内容功能iii：完成，全球化和功率代数
The Ohm-Rush content function III: Completion, globalization, and power-content algebras
论文作者
论文摘要
一个人说，如果扩展与理想的任意相交，或者如果对于s $中的任何元素$ f \，则有同等的$ r $的$ r $，其扩展到$ s $ f $，称为$ f $，称为$ f $ f $ f $ f $ f $。对于Noetherian本地戒指，我们分析完成地图是否为Ohm-Rush。我们证明答案通常是“是”，但在更高的维度中``否''，在任何情况下，它与具有良好代数属性的内容映射一致。然后，我们分析了一个问题，即何时在一维noetherian域上忠实地平面模块和代数中全球化的欧姆 - 卢斯财产全球化，最终在积极的结果和反例中达到了最终。最后，我们介绍了一个概念，即我们严格显示在Ohm-Rush属性和弱内容代数属性之间。
One says that a ring homomorphism $R \rightarrow S$ is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element $f\in S$, there is a unique smallest ideal of $R$ whose extension to $S$ contains $f$, called the content of $f$. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically `yes' in dimension one, but `no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.
