Finiteness of elasticities of orders in central simple algebras
Tom 206 / 2022
Streszczenie
Let be an order in a central simple algebra A over a number field. The elasticity \rho (\mathcal O) is the supremum of all fractions k/l such that there exists a non-zero-divisor a \in \mathcal O that has factorizations into atoms (irreducible elements) of lengths k and l. We characterize the finiteness of the elasticity for Hermite orders \mathcal O if either \mathcal O is a quaternion order, or \mathcal O is an order in a central simple algebra of larger dimension and \mathcal O_{\mathfrak p} is a tiled order at every finite place \mathfrak p at which A_{\mathfrak p} 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.