The Bass and topological stable ranks of the Bohl algebra are infinite

TL;DR

This paper proves that both the Bass stable rank and the topological stable rank of the Bohl algebra are infinite, highlighting its complex algebraic and topological structure.

Contribution

It establishes the infinite nature of the Bass and topological stable ranks for the Bohl algebra, a novel result in the study of this algebraic structure.

Findings

Bass stable rank of Bohl algebra is infinite

Topological stable rank of Bohl algebra is infinite

Uses topology of uniform convergence in analysis

Abstract

The Bohl algebra $\textrm{B}$ is the ring of linear combinations of functions $t^k e^{\lambda t}$, where $k$ is any nonnegative integer, and $\lambda$ is any complex number, with pointwise operations. We show that the Bass stable rank and the topological stable rank of $\textrm{B}$ (where we use the topology of uniform convergence) are infinite.