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Divisorial ideals and v-class semigroups of strictly closed domains
Abstract
We study divisorial ideals and the v-class semigroup of a Noetherian domain satisfying Serre's condition (S2). We prove that strict closedness is equivalent to Clifford v-regularity and describe the structure of the associated v-class semigroup. We use these results to characterize finite generation of the class semigroup and Boole v-regularity. We also construct prime ideal decompositions of integrally closed divisorial ideals and clarify the relationship between these decompositions and local Boole v-regularity. Finally, we study polynomial extensions and use them to construct Boole v-regular and locally Boole v-regular domains in arbitrary dimension.
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BibTeX
@misc{isobe2026divisorial,
title = {{Divisorial ideals and $v$-class semigroups of strictly closed domains}},
author = {Ryotaro Isobe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32134},
eprint = {2610.32134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32134},
}
RIS
TY - UNPB
TI - Divisorial ideals and v-class semigroups of strictly closed domains
AU - Ryotaro Isobe
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32134
UR - https://arxiv.org/abs/2610.32134
AB - We study divisorial ideals and the v-class semigroup of a Noetherian domain satisfying Serre's condition (S_2). We prove that strict closedness is equivalent to Clifford v-regularity and describe the structure of the associated v-class semigroup. We use these results to characterize finite generation of the class semigroup and Boole v-regularity. We also construct prime ideal decompositions of integrally closed divisorial ideals and clarify the relationship between these decompositions and local Boole v-regularity. Finally, we study polynomial extensions and use them to construct Boole v-regular and locally Boole v-regular domains in arbitrary dimension.
ER -