Stable finiteness of monoid algebras and surjunctivity
arxiv(2024)
摘要
A monoid M is said to be surjunctive if every injective cellular automaton
with finite alphabet over M is surjective. We show that monoid algebras of
surjunctive monoids are stably finite. In other words, given any field K and
any surjunctive monoid M, every one-sided invertible square matrix with
entries in the monoid algebra K[M] is two-sided invertible. Our proof uses
first-order model theory.
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