Semigroups of transformations whose characters belong to a given semigroup

Mosarof Sarkar, Shubh N. Singh

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i:i\in I\}$ a partition of $X$. Denote by $T(X)$ the full transformation semigroup on $X$, and $T(X,\mathcal{P})$ the subsemig…