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• W2080753152 abstract "Let $mathcal O$ be a holomorphy ring in a global field $K$, and $R$ a classical maximal $mathcal O$-order in a central simple algebra over $K$. We study sets of lengths of factorizations of cancellative elements of $R$ into atoms (irreducibles). In a large majority of cases there exists a transfer homomorphism to a monoid of zero-sum sequences over a ray class group of $mathcal O$, which implies that all the structural finiteness results for sets of lengths---valid for commutative Krull monoids with finite class group---hold also true for $R$. If $mathcal O$ is the ring of algebraic integers of a number field $K$, we prove that in the remaining cases no such transfer homomorphism can exist and that several invariants dealing with sets of lengths are infinite." @default.
• W2080753152 created "2016-06-24" @default.
• W2080753152 creator A5069431545 @default.
• W2080753152 date "2013-09-01" @default.
• W2080753152 modified "2023-10-03" @default.
• W2080753152 title "Sets of lengths in maximal orders in central simple algebras" @default.
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• W2080753152 doi "https://doi.org/10.1016/j.jalgebra.2013.05.016" @default.
• W2080753152 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/4986414" @default.
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