Green's relations and unit-regularity for semigroup of transformations whose characters are bijective

Mosarof Sarkar, Shubh N. Singh

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i:i\in I\}$ be a partition of $X$. Denote by $T(X,\mathcal{P})$ the semigroup of all transformations of $X$ that preserve $\ma…