The Bass and topological stable ranks for algebras of almost periodic functions on the real line
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- by Raymond Mortini and Rudolf Rupp PDF
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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 $\textrm {AP}_\Lambda =\{f\in \textrm {AP}: \sigma (f)\subseteq \Lambda \}$ 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.References
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Additional Information
- Raymond Mortini
- Affiliation: Département de Mathématiques et Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, Ile du Saulcy, F-57045 Metz, France
- Email: Raymond.Mortini@univ-lorraine.fr
- Rudolf Rupp
- Affiliation: Fakultät für Angewandte Mathematik, Physik und Allgemeinwissenschaften, TH-Nürnberg, Kesslerplatz 12, D-90489 Nürnberg, Germany
- Email: Rudolf.Rupp@th-nuernberg.de
- Received by editor(s): November 14, 2013
- Received by editor(s) in revised form: January 27, 2014
- Published electronically: July 22, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3059-3073
- MSC (2010): Primary 46J10; Secondary 42A75, 30H05
- DOI: https://doi.org/10.1090/tran/6398
- MathSciNet review: 3451869