On the Anderson-Badawi $\omega_{R[X]}(I[X])=\omega_R(I)$ conjecture

DOI10.5817/AM2016-2-71zbMath1374.13007arXiv1401.0459WikidataQ122915047 ScholiaQ122915047MaRDI QIDQ2828834

Peyman Nasehpour

Publication date: 26 October 2016

Published in: Archivum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.0459

zbMATH Keywords

polynomial ringPrüfer domainArmendariz ringGaussian ring\(n\)-absorbing idealGaussian algebrastrongly \(n\)-absorbing idealcontent algebraArmendariz algebraDedekind-Mertens content formula

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (12)

Gaussian elements of a semicontent algebra ⋮ Amount algebras ⋮ The radical of an \(n\)-absorbing ideal ⋮ Absorbing Ideals in Commutative Rings: A Survey ⋮ On Anderson-Badawi conjectures ⋮ The Ohm-Rush content function III: Completion, globalization, and power-content algebras ⋮ On n-absorbing and strongly n-absorbing ideals of amalgamation ⋮ The Ohm–Rush content function II. Noetherian rings, valuation domains, and base change ⋮ n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey ⋮ A proof of the Anderson-Badawi \(\operatorname{rad}(I)^n\subseteq I\) formula for \(n\)-absorbing ideals ⋮ On n-absorbing ideals and (m,n)-closed ideals in trivial ring extensions of commutative rings ⋮ On \(n\)-absorbing ideals of locally divided commutative rings

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