Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective.  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 surjunctive.  also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand,  show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive.
['Tullio Ceccherini-Silberstein', 'Michel Coornaert']
I am writing a research paper on a idea On surjunctive monoids
[{"from": "human", "value": "I am writing a research paper on a idea On surjunctive monoids"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective.  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 surjunctive.  also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand,  show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-surjunctive."}]