Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(1): 153-161

Printed January 31, 2016

https://doi.org/10.4134/BKMS.2016.53.1.153

Copyright © The Korean Mathematical Society.

Some curiosities of the algebra of bounded Dirichlet series

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