alexa Sets of lengths in maximal orders in central simple algebras.
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Smertnig D

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Abstract Let [Formula: see text] be a holomorphy ring in a global field K, and R a classical maximal [Formula: see text]-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 [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 for R. If [Formula: see text] 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.
This article was published in J Algebra and referenced in Journal of Generalized Lie Theory and Applications

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