On finite molecularization domains

Hetzel, Andrew J.; Lawson, Anna L.; Reinhart, Andreas

doi:10.1216/jca.2021.13.69

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On the Monoid Of Nonzero Ideals Of Polynomial Rings1

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2022

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Cited by 2 publications

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“…Example 5.7.1 was already settled in [48,Proposition 4.6], but our techniques allow us to study larger classes of polynomial ideals over arbitrary domains (see Proposition 5.10). For m ∈ N 0 , let M m;1,2 denote the set of all monomials of the form X r 1 X s 2 with r + s = m and r, s ∈ N 0 .…”

Section: On the Monoid Of Nonzero Ideals Of Polynomial Ringsmentioning

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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Section: On the Monoid Of Nonzero Ideals Of Polynomial Ringsmentioning

confidence: 99%