Ideals in semigroups of partial transformations with invariant set (Q6618874)

In the paper, the authors investigate ideals and their structural properties in the context of two generalizations of the partial transformation semigroup. Considering a non-empty set \( X \), they study the foundational framework of \( T(X) \), where \( T(X) \) represents the full transformation semigroup on \( X \) under the composition of functions. They observe that any semigroup can be viewed as an isomorphic subsemigroup of \( T(X) \). Furthermore, the paper provides a comprehensive exploration of \( T(X) \) and as a result, principal, maximal and minimal ideals in such semigroups are examined within this structure. The results presented are supported by relevant examples and the paper includes a resourceful and updated reference list at its conclusion.