A classification of maximal idempotent-generated subsemigroups of finite orientation-preserving singular partial transformation semigroups

In this paper we describe the maximal idempotent-generated subsemigroups of the finite orientation-preserving singular partial transformation semigroup SPOP _n and obtain their complete classification. We also obtain a classification of the maximal idempotent-generated subsemigroups of the finite order-preserving singular partial transformation semigroup PO^k_n\mathit{PO}^{k}_{n} with respect to ≤ _k .