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Richard Brown (2006)
THE ALGEBRAIC ENTROPY OF THE SPECIAL LINEAR CHARACTER AUTOMORPHISMS OF A FREE GROUP ON TWO GENERATORSTransactions of the American Mathematical Society, 359
J. Peters (1979)
Entropy on discrete abelian groupsAdvances in Mathematics, 33
Michael Weiss (1974)
Algebraic and other entropies of group endomorphismsMathematical systems theory, 8
A. Corner (1963)
Every Countable Reduced Torsion-Free Ring is an Endomorphism RingProceedings of The London Mathematical Society
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.
Forum Mathematicum – de Gruyter
Published: Jul 1, 2009
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