On the distribution of prime divisors in Krull monoid algebras

Victor Fadinger; Daniel Windisch

doi:10.1016/j.jpaa.2021.106887

On the distribution of prime divisors in Krull monoid algebras

Victor Fadinger^*, Daniel Windisch

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

In the present work, we prove that every class of the divisor class group of a Krull monoid algebra contains infinitely many prime divisors. Several attempts to this result have been made in the literature so far, unfortunately with open gaps. We present a complete proof of this fact.

Original language	English
Article number	106887
Journal	Journal of Pure and Applied Algebra
Volume	226
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2021.106887
Publication status	Published - 2022

Keywords

Class group
Krull domain
Krull monoid
Monoid algebra
Prime divisors
Semigroup ring

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2021.106887Licence: CC BY 4.0

Cite this

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title = "On the distribution of prime divisors in Krull monoid algebras",

abstract = "In the present work, we prove that every class of the divisor class group of a Krull monoid algebra contains infinitely many prime divisors. Several attempts to this result have been made in the literature so far, unfortunately with open gaps. We present a complete proof of this fact.",

keywords = "Class group, Krull domain, Krull monoid, Monoid algebra, Prime divisors, Semigroup ring",

author = "Victor Fadinger and Daniel Windisch",

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language = "English",

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AU - Windisch, Daniel

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AB - In the present work, we prove that every class of the divisor class group of a Krull monoid algebra contains infinitely many prime divisors. Several attempts to this result have been made in the literature so far, unfortunately with open gaps. We present a complete proof of this fact.

KW - Class group

KW - Krull domain

KW - Krull monoid

KW - Monoid algebra

KW - Prime divisors

KW - Semigroup ring

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U2 - 10.1016/j.jpaa.2021.106887

DO - 10.1016/j.jpaa.2021.106887

M3 - Article

SN - 1873-1376

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 4

M1 - 106887

ER -

On the distribution of prime divisors in Krull monoid algebras

Abstract

Keywords

ASJC Scopus subject areas

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