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A general notion of algebraic entropy and the rank-entropy
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Luigi Salce
Published/Copyright:
June 15, 2009
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.
Received: 2007-06-25
Published Online: 2009-06-15
Published in Print: 2009-July
© de Gruyter 2009
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- Mahler measure under variations of the base group
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Articles in the same Issue
- The Noether Map I
- A general notion of algebraic entropy and the rank-entropy
- Computing the maximal algebra of quotients of a Lie algebra
- Mahler measure under variations of the base group
- Extremal α-pseudocompact abelian groups
- Group algebras whose symmetric and skew elements are Lie solvable
- Walks on graphs and lattices – effective bounds and applications
- Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions
- On the homotopy type of the non-completed classifying space of a p-local finite group
