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A general notion of algebraic entropy and the rank-entropy

A general notion of algebraic entropy and the rank-entropy We give a general definition of a subadditive invariant i of Mod( R ), where R is any ring, and the related notion of algebraic entropy of endomorphisms of R -modules, with respect to i . We examine the properties of the various entropies that arise in different circumstances. Then we focus on the rank-entropy, namely the entropy arising from the invariant ‘rank’ for Abelian groups. We show that the rank-entropy satisfies the Addition Theorem. We also provide a uniqueness theorem for the rank-entropy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

A general notion of algebraic entropy and the rank-entropy

Forum Mathematicum , Volume 21 (4) – Jul 1, 2009

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References (4)

Publisher
de Gruyter
Copyright
© de Gruyter 2009
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORUM.2009.029
Publisher site
See Article on Publisher Site

Abstract

We give a general definition of a subadditive invariant i of Mod( R ), where R is any ring, and the related notion of algebraic entropy of endomorphisms of R -modules, with respect to i . We examine the properties of the various entropies that arise in different circumstances. Then we focus on the rank-entropy, namely the entropy arising from the invariant ‘rank’ for Abelian groups. We show that the rank-entropy satisfies the Addition Theorem. We also provide a uniqueness theorem for the rank-entropy.

Journal

Forum Mathematicumde Gruyter

Published: Jul 1, 2009

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