On surjunctive monoids

Michel Coornaert (1) , Tullio Ceccherini-Silberstein (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Dipartimento di Ingegneria [Benevento]

A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunc- tive. We also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand, we show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive.

Mots clés: Monoid; uniform space; cellular automaton; marked monoid; surjunctive monoid.

Domaines: Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]; Théorie de l'information et codage [math.IT]

Michel Coornaert, Tullio Ceccherini-Silberstein. On surjunctive monoids. International Journal of Algebra and Computation, 2015, 25 (4), pp.567-606. ⟨10.1142/S0218196715500113⟩. ⟨hal-01155378⟩