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

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.

Cited by in corpus (8)

• Factorization theory: From commutative to noncommutative settings
• Sets of lengths in maximal orders in central simple algebras
• Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics
• Factorizations in bounded hereditary Noetherian prime rings
• Factorizations in upper triangular matrices over information semialgebras
• The catenary degree of Krull monoids II
• Factorization under Local Finiteness Conditions
• On noncommutative bounded factorization domains and prime rings