论文标题
代数和离散几何形状的不变链
Invariant chains in algebra and discrete geometry
论文作者
论文摘要
我们将增加链（当地情况）的锥体，单粒和理想的有限产生与相应极限对象的有限生成（全球情况）联系起来。对于锥体和单粒子，没有像理想的情况那样具有noterian性的类似物，我们在示例中证明了这一点。作为一种补救措施，我们发现有限产生的局部全球通信。这些结果来自一个更通用的框架，该框架将封闭操作下的有限发电与在一般地图家族的一般家族下的有限产生相关联。我们还提供了一个新的证据，表明理想的非饱和Inc不变链稳定，缩小了文献中的差距。
We relate finite generation of cones, monoids, and ideals in increasing chains (the local situation) to equivariant finite generation of the corresponding limit objects (the global situation). For cones and monoids there is no analog of Noetherianity as in the case of ideals and we demonstrate this in examples. As a remedy, we find local-global correspondences for finite generation. These results are derived from a more general framework that relates finite generation under closure operations to equivariant finite generation under general families of maps. We also give a new proof that non-saturated Inc-invariant chains of ideals stabilize, closing a gap in the literature.
