发表机构
Vinh University; Institute of Mathematics Vietnam Academy of Science and Technology; FPT University（荣市大学; 越南科学技术院数学研究所; FPT大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究交换 Noether 局部环间平坦局部同态下 Buchsbaum 模与广义 Cohen - Macaulay 模的升降，以及特定条件下有限生成\(R -\)模与其张量积\(M\otimes_RS\)参数理想的关系。
AI 中文摘要
设\((R,\mathfrak{m})\)和\((S,\mathfrak{n})\)为交换 Noether 局部环，\(\varphi: R\to S\)为平坦局部同态。本文首先通过平坦扩张\(\varphi\)刻画 Buchsbaum 模与广义 Cohen - Macaulay 模的升降。然后，在\(\mathfrak{n} = \mathfrak{m}S\)假设下，给出有限生成\(R -\)模\(M\)及其与\(M\otimes_RS\)参数理想间的关系。
英文摘要
Let $(R,\frak m)$ and $(S, \frak n)$ be commutative Noetherian local rings, let $φ: R\to S$ be a flat local homomorphism. In this paper, we first characterize the ascent and descent of Buchsbaum modules and generalized Cohen-Macaulay modules via the flat extension $φ$. Then, we provide relationships between the parameter ideals of a finitely generated $R$-module $M$ and those of $M\otimes_RS$ under the assumption that $\frak{n} = \frak{m} S.$
Comments10 pages, rewrite Question 2.10, comments welcome
