## Banach Journal of Mathematical Analysis

### The Bass and topological stable ranks for algebras of almost periodic functions on the real line, II

#### Abstract

Let $\Lambda$ be either a subgroup of the integers ${\mathbb{Z}}$, a semigroup in ${\mathbb{N}}$, or $\Lambda={\mathbb{Q}}$ (resp., ${\mathbb{Q}}^{+}$). We determine the Bass and topological stable ranks of the algebras $\mathrm{AP}_{\Lambda}=\{f\in\mathrm{AP}:\sigma(f)\subseteq\Lambda\}$ of almost periodic functions on the real line and with Bohr spectrum in $\Lambda$. This answers a question in the first part of this series of articles under the same heading, where it was shown that, in contrast to the present situation, these ranks were infinite for each semigroup $\Lambda$ of real numbers for which the ${\mathbb{Q}}$-vector space generated by $\Lambda$ had infinite dimension.

#### Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 565-581.

Dates
Accepted: 26 December 2018
First available in Project Euclid: 1 March 2019

https://projecteuclid.org/euclid.bjma/1551409236

Digital Object Identifier
doi:10.1215/17358787-2018-0051

Mathematical Reviews number (MathSciNet)
MR3978937

Zentralblatt MATH identifier
07083761

#### Citation

Mortini, Raymond; Sasane, Amol. The Bass and topological stable ranks for algebras of almost periodic functions on the real line, II. Banach J. Math. Anal. 13 (2019), no. 3, 565--581. doi:10.1215/17358787-2018-0051. https://projecteuclid.org/euclid.bjma/1551409236

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