On hopfian cofinite subsemigroups

2013/07/26 by Victor Maltcev, Nik Ruškuc, Maltcev, Victor +2
Computer Science · Decision Sciences · Mathematics · #10M05 #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:10M05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1307.6929

arxiv created 2013/07/26 · openalex publication_date 2013/07/26 · arxiv updated 2013/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On finite complete rewriting systems and large subsemigroups

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