2024/05/28 by Ceccherini-Silberstein, Tullio, Coornaert, Michel, Phung, Xuan Kien · 1 citation
#03C98 #16S36 #20M25 #20M35 #37B15 #68Q80 #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2405.18287
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.