On nilpotent subsemigroups in some matrix semigroups
  We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup $\Omega_n$ of all $n\times n$ real matrices with non-negative coefficients and the semigroup $\mathbf{D}_n$ of all doubly stochastic real matrices. 
Olexandr Ganyushkin and Volodymyr Mazorchuk