A construction of a finitely presented semigroup containing nonnilpotent   nil ideal
  This work presents an example of a finitely presented semigroup $S$ containing an infinite nonnilpotent nil ideal $LS$, whose elements do not have a square (i.e. any word of the type $LXYYZ$ equals zero.) 
Ilya Ivanov-Pogodaev, Sergey Malev
math.RA