Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Algebraic shift equivalence and primitive matrices
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by Mike Boyle and David Handelman
Trans. Amer. Math. Soc. 336 (1993), 121-149
DOI: https://doi.org/10.1090/S0002-9947-1993-1102219-4

Abstract:

Motivated by symbolic dynamics, we study the problem, given a unital subring $S$ of the reals, when is a matrix $A$ algebraically shift equivalent over $S$ to a primitive matrix? We conjecture that simple necessary conditions on the nonzero spectrum of $A$ are sufficient, and establish the conjecture in many cases. If $S$ is the integers, we give some lower bounds on sizes of realizing primitive matrices. For Dedekind domains, we prove that algebraic shift equivalence implies algebraic strong shift equivalence.
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 121-149
  • MSC: Primary 58F03; Secondary 28D20, 46L99, 54H20
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1102219-4
  • MathSciNet review: 1102219