Free monoids are coherent
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.
Citation
Gould , V , Hartmann , M & Ruskuc , N 2017 , ' Free monoids are coherent ' , Proceedings of the Edinburgh Mathematical Society , vol. 60 , no. 1 , pp. 127-131 . https://doi.org/10.1017/S0013091516000079
Publication
Proceedings of the Edinburgh Mathematical Society
Status
Peer reviewed
ISSN
0013-0915Type
Journal article
Rights
© 2015, Edinburgh Mathematical Society. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at journals.cambridge.org / https://dx.doi.org/10.1017/S0013091516000079
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