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arXiv · 1412.7340

Free monoids are coherent

Victoria Gould·Miklos Hartmann·Nik Ruskuc
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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.

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Victoria Gould, Miklos Hartmann, Nik Ruskuc. 2014-12-23. Free monoids are coherent. https://arxiv.org/abs/1412.7340

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