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arXiv · 1307.6929

On hopfian cofinite subsemigroups

Victor Maltcev·N. Ruskuc
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Abstract

If a finitely generated semigroup S has a hopfian (meaning: every surjective endomorphism is an automorphism) cofinite subsemigroup T then S is hopfian too. This no longer holds if S is not finitely generated. There exists a finitely generated hopfian semigroup S with a non-hopfian subsemigroup T such that S\T has size 1.

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Victor Maltcev, N. Ruskuc. 2013-07-26. On hopfian cofinite subsemigroups. https://arxiv.org/abs/1307.6929

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