Core of ideals in one-dimensional Noetherian domains

DOI10.1016/j.jalgebra.2020.02.023zbMath1436.13003OpenAlexW3015145891MaRDI QIDQ2174546

Salah-Eddine Kabbaj, Abdeslam Mimouni

Publication date: 21 April 2020

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2020.02.023

zbMATH Keywords

stabilityreductionNoetherian domaincore of an idealtrace property

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items

Minimal reductions and core of ideals in pullbacks, Reductions and cores of ideals in trivial ring extensions, Reductions and Core of Ideals in Integral Domains: Some Recent Developments

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Factoring ideals in integral domains
• The core of ideals in arbitrary characteristic
• The core of zero-dimensional monomial ideals
• Core of ideals in integral domains
• Domains satisfying the trace property
• The radical trace property
• General elements and joint reductions
• When the dual of an ideal is a ring
• Globalizing local properties of Prüfer domains
• Coherentlike conditions in pullbacks
• Class semigroups of integral domains
• A formula for the core of an ideal
• The radical trace property and primary ideals
• Cores of ideals in 2-dimensional regular local rings
• A formula for the core of certain strongly stable ideals
• Intersections of quotient rings of an integral domain
• Reflexive domains
• Overrings and divisorial ideals of rings of the form \(D+M\)
• On the ubiquity of Gorenstein rings
• Core and residual intersections of ideals
• Annihilators of graded components of the canonical module, and the core of standard graded algebras
• Reductions of Ideals in Prufer Domains
• Pairs of Rings with the Same Prime Ideals
• On a non-vanishing conjecture of Kawamata and the core of an ideal
• Divisorial domains
• ON THE STRUCTURE OF STABLE DOMAINS
• Note on the divisoriality of domains of the form $k[[X^{p}, X^{q}]$, $k[X^{p}, X^{q}]$, $k[[X^{p}, X^{q}, X^{r}]]$, and $k[X^{p}, X^{q}, X^{r}]$]
• On the core of ideals
• Generators of reductions of ideals in a local Noetherian ring with finite residue field
• t-class semigroups of integral domains
• Integral domains in which each non‐zero ideal is divisorial
• Stable rings and a problem of Bass
• Reductions of Ideals in Commutative Rings
• On the classification of stable domains
• The structure of the core of ideals