Document Type

Article

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This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHMATICS

Abstract

We study the endomorphisms ϕ of abelian groups G having a “small” algebraic entropy h (where “small” usually means ). Using essentially elementary tools from linear algebra, we show that this study can be carried out in the group , where an automorphism ϕ with must have all eigenvalues in the open circle of radius 2, centered at 0 and ϕ must leave invariant a lattice in , i.e., be essentially an automorphism of . In particular, all eigenvalues of an automorphism ϕ with must be roots of unity. This is a particular case of a more general fact known as Algebraic Yuzvinskii Theorem. We discuss other particular cases of this fact and we give some applications of our main results.

DOI

10.1016/j.laa.2013.05.021

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Algebra Commons

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