On the integral domains characterized by a Bézout property on intersections of principal ideals

DOI10.1016/j.jalgebra.2021.06.028zbMath1472.13005arXiv2002.00950OpenAlexW3180719483MaRDI QIDQ2049373

Lorenzo Guerrieri, K. Alan Loper

Publication date: 25 August 2021

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

Full work available at URL: https://arxiv.org/abs/2002.00950

zbMATH Keywords

star operationsintersections of principal idealsring constructions

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integral domains of finite \(t\)-character
• Ideal theory of infinite directed unions of local quadratic transforms
• Well behaved prime t-ideals
• Characterizing domains of finite \(*\)-character
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Commutative coherent rings
• Integral domains that satisfy Gauss's lemma
• Flat ideals. II
• On finite conductor domains
• Coherentlike conditions in pullbacks
• The trace of the canonical module
• \(t\)-local domains and valuation domains
• Asymptotic properties of infinite directed unions of local quadratic transforms
• Two conductor theorems
• Finite conductor rings
• When the Semistar Operation is the Identity
• On a property of pre-schreier domains
• Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks
• Directed unions of local monoidal transforms and GCD domains
• Integral Domains in Which Each Ideal Is aW-Ideal