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Classification problems for shifts on modules over a principal ideal domain


Authors: Fabio Fagnani and Sandro Zampieri
Journal: Trans. Amer. Math. Soc. 349 (1997), 1993-2006
MSC (1991): Primary 54C70, 15A23, 93B25
MathSciNet review: 1407487
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Abstract: In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.


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Additional Information

Fabio Fagnani
Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
Email: fagnani@cibs.sns.it

Sandro Zampieri
Affiliation: Dipartimento di Elettronica ed Informatica, Università di Padova, via Gradenigo, 6/a, 35131 Padova, Italy
Email: zampi@paola.dei.unipd.it

DOI: https://doi.org/10.1090/S0002-9947-97-01876-X
Keywords: Shifts, dynamical systems, transitivity, principal ideal domains, polynomial matrices, behavioral approach
Received by editor(s): November 15, 1995
Article copyright: © Copyright 1997 American Mathematical Society