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## Abstract

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 language | English |
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Pages (from-to) | 127-131 |

Number of pages | 5 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 60 |

Issue number | 1 |

Early online date | 15 Jun 2016 |

DOIs | |

Publication status | Published - Feb 2017 |

## Keywords

- Free monoids
- S-acts
- Coherency

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