On hopfian cofinite subsemigroups
classification
🧮 math.GR
keywords
hopfianfinitelygeneratedcofinitesemigroupsubsemigroupautomorphismendomorphism
read the original 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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