Abstract

We prove that a countable dimensional associative algebra (resp. a countable semigroup) of locally subexponential growth is M∞-embeddable as a left ideal in a finitely generated algebra (resp. semigroup) of subexponential growth. Moreover, we provide bounds for the growth of the finitely generated algebra (resp. semigroup). The proof is based on a new construction of matrix wreath product of algebras.

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