Factorization of ideals

Anderson, D. D.; Juett, J. R.; Mooney, Christopher

doi:10.1080/00927872.2018.1517359

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Cited by 8 publications

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“…To mention some classical results, R is a Dedekind domain if and only if I(R) = I * (R) if and only if I(R) is a factorial monoid, and R is a Krull domain if and only if I * v (R) is a factorial monoid. Recent progress in such directions can be found in the work by Anderson, Juett, Klingler, Olberding, Reinhart, and others (e.g., [49,58,3,50,56,57,52]).…”

Section: Introductionmentioning

confidence: 99%

On the arithmetic of monoids of ideals

Geroldinger¹,

Khadam²

2021

Preprint

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We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of r-invertible r-ideals for certain ideal systems r) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetical phenomena with Krull monoids having infinite class group and prime divisors in all classes.

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