On Automatic Rees Matrix Semigroups

Abstract We consider a Rees matrix semigroup S = M[U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that pU 1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.

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