Brauer and Jones tied monoids

We introduce a ramified monoid , attached to each Brauer–type monoid, that is, the symmetric group Jones and Brauer monoids among others. Ramified correspond class of tied arising from knot theory are interesting in themselves. The is Coxeter-like version so–called braid monoid. give presentation Also, we study two tied-like cannot be described as monoids. However, these can also regarded versions