Length functions, multiplicities and algebraic entropy

DOI10.1515/form.2011.117zbMath1286.16002OpenAlexW2079992114MaRDI QIDQ4915086

Peter Vámos, Simone Virili, Luigi Salce

Publication date: 16 April 2013

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

Full work available at URL: https://doi.org/10.1515/form.2011.117

zbMATH Keywords

multiplicitieslength functionsalgebraic entropyendomorphisms of modules

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Ordinary and skew polynomial rings and semigroup rings (16S36) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) General module theory in associative algebras (16D10)

Related Items (29)

Entropy on abelian groups ⋮ Topological entropy for locally linearly compact vector spaces ⋮ Mean dimension, mean rank, and von Neumann-Lück rank ⋮ 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 ⋮ Two new proofs concerning the intrinsic algebraic entropy ⋮ Algebraic entropy for amenable semigroup actions ⋮ A soft introduction to algebraic entropy ⋮ Algebraic entropy for valuation domains ⋮ When the intrinsic algebraic entropy is not really intrinsic ⋮ Multiplicative invariants and length functions over valuation domains ⋮ Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups ⋮ Ore localization of amenable monoid actions and applications toward entropy -- addition formulas and the bridge theorem ⋮ Decomposition and classification of length functions ⋮ Almost Dedekind domains without radical factorization ⋮ Length Functions over Prüfer Domains ⋮ Unnamed Item ⋮ 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 ⋮ Intrinsic algebraic entropy ⋮ Inertial properties in groups ⋮ Some applications of algebraic entropy to the proof of Milnor-Wolf theorem ⋮ A property of the lamplighter group ⋮ Sofic mean length ⋮ Entropy on normed semigroups (towards a unifying approach to entropy) ⋮ Intrinsic valuation entropy ⋮ The Mal'cev Rank for Modules over Pseudo-Valuation Domains

Cites Work

• Adjoint algebraic entropy.
• On \({\mathbb{Z}}\)-valued additive functions on module category
• Algebraic entropy for Abelian groups
• Algebraic and other entropies of group endomorphisms
• A general notion of algebraic entropy and the rank-entropy
• Topological Entropy
• A GENERALIZATION OF THE CONCEPT OF LENGTH
• Algebraic Entropy of Generalized Shifts on Direct Products
• ADDITIVE FUNCTIONS AND DUALITY OVER NOETHERIAN RINGS

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