2021/10/15 by Casper Barendrecht, Barendrecht, Casper
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2110.08047
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let O be an order in a central simple algebra A over a number field. The elasticitity ρ(O) is the supremum of all fractions k/l such that there exists an non-zero-divisor a ∈ O that has factorizations into atoms (irreducible elements) of length k and l. We characterize the finiteness of the elasticity for Hermite orders O, if either O is a quaternion order, or O is an order in an central simple algebra of larger dimension and O_\mathfrakp is a tiled order at every finite place \mathfrakp at which A_\mathfrakp is not a division ring. We also prove a transfer result for such orders. This extends previous results for hereditary orders to a non-hereditary setting.