Demotions of ideals in commutative rings with applications to normally torsion-freeness

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Nasernejad, Mehrdad, Toledo, Jonathan
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866915562807885824
author Nasernejad, Mehrdad
Toledo, Jonathan
author_facet Nasernejad, Mehrdad
Toledo, Jonathan
contents Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals.
format Preprint
id arxiv_https___arxiv_org_abs_2510_16538
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Demotions of ideals in commutative rings with applications to normally torsion-freeness
Nasernejad, Mehrdad
Toledo, Jonathan
Commutative Algebra
Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals.
title Demotions of ideals in commutative rings with applications to normally torsion-freeness
topic Commutative Algebra
url https://arxiv.org/abs/2510.16538