Some curiosities of the algebra of bounded Dirichlet series
Raymond Mortini, Amol Sasane
TL;DR
This paper investigates the algebraic properties of bounded Dirichlet series, revealing complex structural characteristics such as non-coherence, infinite Bass stable rank, and infinite Krull dimension.
Contribution
It demonstrates that the algebra of bounded Dirichlet series is not coherent and has infinite stable ranks and Krull dimension, advancing understanding of its algebraic complexity.
Findings
The algebra of bounded Dirichlet series is not a coherent ring.
It has infinite Bass stable rank.
It has infinite topological stable rank and Krull dimension.
Abstract
It is shown that the algebra 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 the algebra of bounded Dirichlet series has infinite topological stable rank and infinite Krull dimension.
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