PreprintarXiv licencearXiv
Buchsbaum modules and parameter ideals under flat extensions
Abstract
Let (R,frak m) and (S, frak n) be commutative Noetherian local rings, let φ: R→ 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⊗RS under the assumption that frakn = frakm S.
Related
- Counterexamples to Minkowski-type inequalities and the Rees converse for modules via mixed Buchsbaum-Rim Multiplicities
- STRONGLY ϕ-FLAT MODULES, STRONGLY NONNIL-INJECTIVE MODULES AND THEIR HOMOLOGICAL DIMENSIONS
- Reduction numbers under flat extensions
- Reduced and coreduced modules with respect to inverse families of ideals
- Extensions of Restricted Simple Modules for Restricted Lie Algebras of Cartan Type
BibTeX
@misc{loan2026buchsbaum,
title = {{Buchsbaum modules and parameter ideals under flat extensions}},
author = {Nguyen Thi Hong Loan and Le Thanh Nhan and Pham Hung Quy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10393},
eprint = {2607.10393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10393},
}
RIS
TY - UNPB
TI - Buchsbaum modules and parameter ideals under flat extensions
AU - Nguyen Thi Hong Loan
AU - Le Thanh Nhan
AU - Pham Hung Quy
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2607.10393
UR - https://arxiv.org/abs/2607.10393
AB - Let (R,frak m) and (S, frak n) be commutative Noetherian local rings, let φ: R→ 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⊗_RS under the assumption that frakn = frakm S.
ER -