A general notion of algebraic entropy and the rank-entropy

DOI10.1515/FORUM.2009.029zbMath1203.20048OpenAlexW2034040504MaRDI QIDQ5191072

Paolo Zanardo, Luigi Salce

Publication date: 28 July 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2009.029

zbMATH Keywords

endomorphismstorsion-free Abelian groupspure subgroupsfiniteness conditionsalgebraic entropyalgebraic dynamical systemsgrowth of submodulessubadditive invariants

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Morphisms of commutative rings (13B10) Torsion-free groups, infinite rank (20K20) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Subgroups of abelian groups (20K27) Other special types of modules and ideals in commutative rings (13C13)

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Entropy on abelian groups, Topological entropy for locally linearly compact vector spaces, Algebraic entropy of amenable group actions, The addition theorem for algebraic entropies induced by non-discrete length functions, The addition theorem for locally monotileable monoid actions, Algebraic entropy for amenable semigroup actions, A soft introduction to algebraic entropy, Algebraic entropy for valuation domains, Weakly weighted generalised quasi-metric spaces and semilattices, New and old facts about entropy in uniform spaces and topological groups, Entropy in a category, Multiplicative invariants and length functions over valuation domains, Mean dimension of natural extension of algebraic systems, Decomposition and classification of length functions, Length Functions over Prüfer Domains, On Adjoint Entropy of Abelian Groups, The Pinsker subgroup of an algebraic flow, Algebraic Entropies for Abelian Groups with Applications to the Structure of Their Endomorphism Rings: A Survey, Algebraic Entropy in Locally Linearly Compact Vector Spaces, Corner’s Realization Theorems from the Viewpoint of Algebraic Entropy, Length functions, multiplicities and algebraic entropy, Inertial properties in groups, The corank of a flow over the category of linearly compact vector spaces, Some applications of algebraic entropy to the proof of Milnor-Wolf theorem, Sofic mean length, Entropy on normed semigroups (towards a unifying approach to entropy), Intrinsic valuation entropy, Generalized quasi-metric semilattices, The Mal'cev Rank for Modules over Pseudo-Valuation Domains

Cites Work

• Entropy on discrete Abelian groups
• Algebraic entropy
• Algebraic and other entropies of group endomorphisms
• Topological Entropy
• Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring