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June 2013 Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic
Alfred Geroldinger
Osaka J. Math. 50(2): 503-539 (June 2013).

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.

Citation

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Alfred Geroldinger. "Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic." Osaka J. Math. 50 (2) 503 - 539, June 2013.

Information

Published: June 2013
First available in Project Euclid: 21 June 2013

zbMATH: 1279.20073
MathSciNet: MR3080813

Subjects:
Primary: 13F05, 16H10, 20M13

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics

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Vol.50 • No. 2 • June 2013
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