标题： 上同调中的不稳定元素以及Lescot的一个问题 显示英文标题

标题： Unstable elements in cohomology and a question of Lescot

摘要： 在他关于交换诺特局部环 $R$上模的syzygy模的Bass级数的工作中，Lescot引入了一个数值不变量，记为 $\sigma(R)$，并询问对于任何 $R$是否它是有限的。 他证明了当 $R$是Gorenstein或Golod时，这是成立的。 在本工作中，许多新的环类 $R$被确定，对于这些环， $\sigma(R)$是有限的。 新的洞察是$\sigma(R)$与从模的通常上同调到其稳定上同调的自然映射有关，这允许使用乘法结构来研究$\sigma(R)$的有限性问题。 显示英文摘要

摘要： In his work on the Bass series of syzygy modules of modules over a commutative noetherian local ring $R$, Lescot introduces a numerical invariant, denoted $\sigma(R)$, and asks whether it is finite for any $R$. He proves that this is so when $R$ is Gorenstein or Golod. In the present work many new classes of rings $R$ for which $\sigma(R)$ is finite are identified. The new insight is that $\sigma(R)$ is related to the natural map from the usual cohomology of the module to its stable cohomology, which permits the use of multiplicative structures to study the question of finiteness of $\sigma(R)$.