标题： 绝对浅层序列 显示英文标题

标题： Absolutely superficial sequences

摘要： 绝对浅序列由 P. Schenzel 引入，以便研究广义 Cohen-Macaulay（ resp. Buchsbaum）模。 对于任意局部环，它们被证明是 d-序列。 本文建立了与模相关的绝对浅序列的性质。 表明它们与其他在广义 Cohen-Macaulay（ resp. Buchsbaum）模理论中的序列密切相关。 特别是，每个参数理想的 Hilbert-Samuel 函数存在一个上界函数，当且仅当该理想由绝对浅序列生成时，该上界函数被达到。 显示英文摘要

摘要： Absolutely superficial sequences was introduced by P. Schenzel in order to study generalized Cohen-Macaulay (resp. Buchsbaum) modules. For an arbitrary local ring, they turned out to be d-sequences. This paper established properties of absolutely superficial sequences with respect to a module. It is shown that they are closely related to other sequences in the theory of generalized Cohen-Macaulay (resp. Buchsbaum) modules. In particular, there is a bounding function for the Hilbert-Samuel function of every parameter ideal such that this bounding function is attained if and only if the ideal is generated by an absolutely superficial sequence.