Linear cellular automata over modules of finite length and stable finiteness of group rings

DOI10.1016/j.jalgebra.2007.06.035zbMath1127.37015OpenAlexW2004309140MaRDI QIDQ2466943

Michel Coornaert, Tullio G. Ceccherini Silberstein

Publication date: 16 January 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.06.035

zbMATH Keywords

linear cellular automatonsofic groupArtinian moduleNoetherian moduledirect finiteness

Mathematics Subject Classification ID

Geometric group theory (20F65) Cellular automata (computational aspects) (68Q80) Dynamical aspects of cellular automata (37B15) Symbolic dynamics (37B10) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (7)

A geometric generalization of Kaplansky’s direct finiteness conjecture ⋮ Amenability and Linear Cellular Automata Over Semisimple Modules of Finite Length ⋮ On sofic groups, Kaplansky's conjectures, and endomorphisms of pro-algebraic groups ⋮ Surjunctivity and Reversibility of Cellular Automata over Concrete Categories ⋮ Sofic groups and profinite topology on free groups. ⋮ On linear shifts of finite type and their endomorphisms ⋮ Sofic mean length

Cites Work

• Amenable groups and cellular automata
• Endomorphisms of symbolic algebraic varieties
• Sofic groups and direct finiteness.
• Stable finiteness of group rings in arbitrary characteristic
• Injective linear cellular automata and sofic groups
• The Garden of Eden theorem for linear cellular automata
• An Introduction to Symbolic Dynamics and Coding
• On sofic groups
• Left and right inverses in group algebras
• Idempotents in Group Rings
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