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arXiv · 1402.4825

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

Raymond Mortini·Rudolf Rupp
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Abstract

Let $\Lambda$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras ${\rm AP}_\Lambda=\{f\in {\rm AP}: \sigma(f)\subseteq \Lambda\}$ 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 Su\'arez's result for ${\rm AP}_\mathbb R={\rm AP}$. Also considered are general subalgebras of AP.

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Raymond Mortini, Rudolf Rupp. 2014-02-19. The Bass and topological stable ranks for algebras of almost periodic functions on the real line. https://arxiv.org/abs/1402.4825

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