2014/12/23 by Gould, Victoria, Hartmann, Miklos, Ruskuc, Nik
#20M05 #20M30 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1412.7340
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.