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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Divisibility constraints on degrees of factor maps


Author: Paul Trow
Journal: Proc. Amer. Math. Soc. 113 (1991), 755-760
MSC: Primary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1991-1056686-9
MathSciNet review: 1056686
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Abstract: We show that the degree of a finite-to-one factor map $ f:{\sum _A} \to {\sum _B}$ between shifts of finite type is constrained by the factors of $ {\chi _A}$ and $ {\chi _B}$. A special case of these constraints is that if $ ^*B$, then the degree of $ f$ is a unit in $ \mathbb{Z}[1/{\det ^*}B]$ (where $ ^*A$ is the rank of the Jordan form away from 0 of $ A$, and $ {\det ^*}B$ is the determinant of the Jordan form away from 0 of $ B$).


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DOI: https://doi.org/10.1090/S0002-9939-1991-1056686-9
Article copyright: © Copyright 1991 American Mathematical Society