Free monoids are coherent

V Gould, M Hartmann, Nik Ruskuc

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
2 Downloads (Pure)


A monoid S is said to be right coherent if every finitely generated subact of
every finitely presented right S-act is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left coherent. These notions are analogous to those for a ring R (where, of course, S-acts are replaced by R-modules). Choo, Lam and Luft have shown that free rings are coherent. In this note we prove that, correspondingly, any free monoid is coherent, thus answering a question posed by the first author in 1992.

Original languageEnglish
Pages (from-to)127-131
Number of pages5
JournalProceedings of the Edinburgh Mathematical Society
Issue number1
Early online date15 Jun 2016
Publication statusPublished - Feb 2017


  • Free monoids
  • S-acts
  • Coherency


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