<正>LetRbeanassociativeringnotnecessarilypossessinganidentityand(S,≤)astrictlytotallyorderedmonoidwhichisalsoartinianandsatisfiesthat0≤sforanys∈S.AssumethatMisaleftR-modulehavingproperty(F).ItisshownthatMisaco-HopfianleftR-moduleifandonlyif[MS,≤]isaco-Hopfanleft[[RS,≤]]-module.