Some curiosities of the algebra of bounded Dirichlet series
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 153-161
https://doi.org/10.4134/BKMS.2016.53.1.153
Printed January 31, 2016
Raymond Mortini and Amol Sasane
Universit\'{e} de Lorraine, London School of Economics
Abstract : It is shown that the algebra $\sH$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\sH$ has infinite topological stable rank and infinite Krull dimension.
Keywords : coherent ring, Hardy algebra, Dirichlet series, Bass stable rank, topological stable rank, Krull dimension, $K$-theory
MSC numbers : Primary 11M41; Secondary 30H05, 13E99
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