title: Sets of lengths in maximal orders in central simple algebras.
abstract: Let [Formula: see text] be a holomorphy ring in a global fieldK, andRa classical maximal [Formula: see text]-order in a central simple algebra overK. We study sets of lengths of factorizations of cancellative elements ofRinto 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 [Formula: see text], which implies that all the structural finiteness results for sets of lengths-valid for commutative Krull monoids with finite class group-hold also true forR. If [Formula: see text] is the ring of algebraic integers of a number fieldK, we prove that in the remaining cases no such transfer homomorphism can exist and that several invariants dealing with sets of lengths are infinite.
authors: Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria.
authors: Daniel
authors: D
authors: Smertnig
keywords: 11R54; 16H10; 16U30; 20M12; 20M13; Brandt groupoid; Divisorial ideals; Global fields; Krull monoids; Maximal orders; Sets of lengths