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.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 DOI:
 10.48550/arXiv.1412.7340
 arXiv:
 arXiv:1412.7340
 Bibcode:
 2014arXiv1412.7340G
 Keywords:

 Mathematics  Rings and Algebras;
 20M05;
 20M30
 EPrint:
 Minor revision of previous version