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Journal Articles International Journal of Algebra and Computation Year : 2015

On surjunctive monoids

Abstract

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.
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Dates and versions

hal-01155378 , version 1 (26-05-2015)

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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⟩
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