PreprintarXiv licencearXiv
Almost Gorenstein standard graded rings and their localizations
Abstract
We prove that a Cohen-Macaulay standard graded integral domain over a field is almost Gorenstein as a graded ring if and only if the completion of its localization at the graded maximal ideal is almost Gorenstein as a local ring.
Related
- Almost Gorenstein edge rings of bipartite graphs and their h-vectors
- Betti Sequences of Four-Generated Non-Almost-Symmetric Nearly Gorenstein Numerical Semigroup Rings
- Normality of ideals beyond the standard graded setting: families from numerical semigroup rings
- Presentability of categories of localizations and analytic rings
- Grothendieck Rings of Module Categories: Localizations, Strata, and Radicals
BibTeX
@misc{endo2026almost,
title = {{Almost Gorenstein standard graded rings and their localizations}},
author = {Naoki Endo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02767},
eprint = {2610.02767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02767},
}
RIS
TY - UNPB
TI - Almost Gorenstein standard graded rings and their localizations
AU - Naoki Endo
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02767
UR - https://arxiv.org/abs/2610.02767
AB - We prove that a Cohen-Macaulay standard graded integral domain over a field is almost Gorenstein as a graded ring if and only if the completion of its localization at the graded maximal ideal is almost Gorenstein as a local ring.
ER -