Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 50, Number 2 (2013), 503-539.
Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic
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.
Osaka J. Math. Volume 50, Number 2 (2013), 503-539.
First available in Project Euclid: 21 June 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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