Tied monoids

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups their relatives acting on of set partitions. The nature our indicate that they should give origin new knot algebras; indeed, include the monoid singular monoid, which were used, respectively, polynomial invariants for classical links links. Consequently, we provide a mechanism attach an algebra each monoid; this not only captures known generalizations bt-algebra, but also produces possible algebras. To build it is necessary have presentations partition types A, B D, among others. For type A use presentation due FitzGerald other was them.