PreprintCC BY 4.0arXiv
Reduction numbers under flat extensions
Abstract
The reduction number of the maximal ideal of a localization (or even faithfully flat extension) need not increase under specialization. Nevertheless, for each fixed local ring the reduction numbers of the maximal ideals of all its localization have a finite common bound.
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BibTeX
@misc{asgharzadeh2026reduction,
title = {{Reduction numbers under flat extensions}},
author = {Mohsen Asgharzadeh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41659},
eprint = {2610.41659},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41659},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reduction numbers under flat extensions
AU - Mohsen Asgharzadeh
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41659
UR - https://arxiv.org/abs/2610.41659
AB - The reduction number of the maximal ideal of a localization (or even faithfully flat extension) need not increase under specialization. Nevertheless, for each fixed local ring the reduction numbers of the maximal ideals of all its localization have a finite common bound.
ER -