On finite presentability of Bruck-Reilly extensions of a monoid with respect to an endomorphism and its powers.

Carvalho, Catarina and Ruskuc, Nik (2007) On finite presentability of Bruck-Reilly extensions of a monoid with respect to an endomorphism and its powers. Algebra Colloquium (3). pp. 389-402.
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Let M be a monoid and let θ be an endomorphism of M. We prove that if the Bruck–Reilly extension BR(M, θ) is finitely presented, then the Bruck–Reilly extension BR(M, θm) is also finitely presented for all m ⩾ 1

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