Article ID Journal Published Year Pages File Type
6414867 Journal of Algebra 2013 43 Pages PDF
Abstract

Let O be a holomorphy ring in a global field K, and R a classical maximal 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 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 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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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