Osaka Journal of Mathematics

Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic

Alfred Geroldinger

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Abstract

A (not necessarily commutative) Krull monoid---as introduced by Wauters---is defined as a completely integrally closed monoid satisfying the ascending chain condition on divisorial two-sided ideals. We study the structure of these Krull monoids, both with ideal theoretic and with divisor theoretic methods. Among others we characterize normalizing Krull monoids by divisor theories. Based on these results we give a criterion for a Krull monoid to be a bounded factorization monoid, and we provide arithmetical finiteness results in case of normalizing Krull monoids with finite Davenport constant.

Article information

Source
Osaka J. Math. Volume 50, Number 2 (2013), 503-539.

Dates
First available in Project Euclid: 21 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1371833498

Mathematical Reviews number (MathSciNet)
MR3080813

Zentralblatt MATH identifier
1279.20073

Subjects
Primary: 20M13: Arithmetic theory of monoids 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 16H10: Orders in separable algebras

Citation

Geroldinger, Alfred. Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic. Osaka J. Math. 50 (2013), no. 2, 503--539. https://projecteuclid.org/euclid.ojm/1371833498.


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