Ideal containment in commutative rings

DOI10.1142/S0219498823502006arXiv2111.00761OpenAlexW3208791554MaRDI QIDQ6168147

Abdeslam Mimouni

Publication date: 8 August 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.00761

zbMATH Keywords

pullbacksreduction of idealsbasic idealtrivial ring extensionbig idealbig ideal ringC-idealupper big deal

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Class groups (13C20)

Cites Work

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• Idealization of a module
• Strongly divisorial ideals and complete integral closure of an integral domain
• The \(D+XD_ s[X\) construction from GCD-domains]
• On Jaffard domains
• Topologically defined classes of commutative rings
• Commutative coherent rings
• \(D+M\) constructions with general overrings
• Pseudo-valuation domains
• The construction \(D+XD_s[X\)]
• Coherentlike conditions in pullbacks
• On the class group and the local class group of a pullback
• Overrings and divisorial ideals of rings of the form \(D+M\)
• Trivial Extensions Defined by Coherent-like Conditions
• On a class of mori domains
• The ratliff-rush ideals in a noetherian ring
• Reductions of Ideals in Prufer Domains
• Pairs of Rings with the Same Prime Ideals
• On the prime spectrum of a mori domain
• Divisorial 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 $k[X^{p}, X^{q}, X^{r}]$]
• Trace Properties and Pullbacks
• Various Facets of Rings BetweenD[X andK[X]]
• The u,u⁻¹lemma revisited
• Reductions of Ideals in Commutative Rings

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