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arXiv · 2607.10393

Buchsbaum modules and parameter ideals under flat extensions

Nguyen Thi Hong Loan·Le Thanh Nhan·Pham Hung Quy
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Abstract

Let $(R,\frak m)$ and $(S, \frak n)$ be commutative Noetherian local rings, let $\varphi: R\to S$ 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 $\varphi$. 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 $\frak{n} = \frak{m} S.$

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Nguyen Thi Hong Loan, Le Thanh Nhan, Pham Hung Quy. 2026-07-11. Buchsbaum modules and parameter ideals under flat extensions. https://arxiv.org/abs/2607.10393

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