Ideal lattices of semigroup of doubly stochastic matrices

In this paper we illustrate the rule for finding number of idempotents in the doubly stochastic matrix $D_n$ and also locate the idempotents for the semigroups $D_3$ and $D_4$. Further describe idempotent generated ideals of these semigroups and it is shown that these idempotent generated ideals form lattices.