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
Collections
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