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

Mortini, Raymond; Rupp, Rudolf

doi:10.1090/tran/6398

The Bass and topological stable ranks for algebras of almost periodic functions on the real line
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Trans. Amer. Math. Soc. 368 (2016), 3059-3073 Request permission

Abstract:

Let $\Lambda$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras $\textrm {AP}_\Lambda =\{f\in \textrm {AP}: \sigma (f)\subseteq \Lambda \}$ of almost periodic functions on the real line and with Bohr spectrum in $\Lambda$ are infinite whenever the algebraic dimension of the $\mathbb {Q}$-vector space generated by $\Lambda$ is infinite. This extends Suárez’s result for $\textrm {AP}_\mathbb {R}=\textrm {AP}$. Also considered are general subalgebras of AP.

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