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PreprintCC BY 4.0arXiv

The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions

  • Tran Do Minh Chau
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Abstract

This paper deals with certain classes of modules under module-finite extensions. Let φ: R↪ S be a module-finite extension between commutative Noetherian local rings. We investigate the transfer of Artinian module structures and attached primes between R and S. We clarify the behavior of local cohomology modules as well as certain structures of finitely generated S-modules under the restriction of scalars to R via φ. We show that R is a quotient of a Cohen-Macaulay local ring if and only if so is S. As an application, we characterize the structure of Nagata's idealization. Using Macaulayfication of algebraic varieties and idealization, we give an example to illustrate the results.

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Cite

BibTeXRIS
BibTeX
@misc{chau2026transfer,
  title = {{The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions}},
  author = {Tran Do Minh Chau},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11003},
  eprint = {2609.11003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11003},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The transfer of Artinian and Cohen-Macaulay properties under module-finite extensions
AU  - Tran Do Minh Chau
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11003
UR  - https://arxiv.org/abs/2609.11003
AB  - This paper deals with certain classes of modules under module-finite extensions. Let φ: R↪ S be a module-finite extension between commutative Noetherian local rings. We investigate the transfer of Artinian module structures and attached primes between R and S. We clarify the behavior of local cohomology modules as well as certain structures of finitely generated S-modules under the restriction of scalars to R via φ. We show that R is a quotient of a Cohen-Macaulay local ring if and only if so is S. As an application, we characterize the structure of Nagata's idealization. Using Macaulayfication of algebraic varieties and idealization, we give an example to illustrate the results.
ER  -