A characterization of length-factorial Krull monoids

Abstract

An atomic monoid is length-factorial if each two distinct factorizations of any element have distinct factorization lengths. We provide a characterization of length-factorial Krull monoids in terms of their class groups and the distribution of prime divisors in the classes.

arXiv commentTo appear in New York Journal of Mathematics

References in corpus (4)

• Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids
• Factorizations of Elements in Noncommutative Rings: A Survey
• Factoriality and class groups of cluster algebras
• On congruence half-factorial Krull monoids with cyclic class group

Cited by in corpus (4)

• On the additive structure of algebraic valuations of polynomial semirings
• Factorization under Local Finiteness Conditions
• Length-Factoriality and Pure Irreducibility
• On transfer Krull monoids