On the monoid of all injective orientation-preserving and extensive partial transformations
De Biao Li, Wen Ting Zhang, Yanfeng Luo · Communications in Algebra · 2021
Let POPEIn be the monoid of all injective orientation-preserving and extensive partial transformations on {1,2,…,n} ordered in the standard way. In this paper, we determine the minimum generating set and the minimum quasi-idempotent generating set of POPEIn, and so the rank and the quasi-idempotent rank of POPEIn are obtained. Moreover, we describe the maximal subsemigroups and maximal quasi-idempotent generated subsemigroups of POPEIn and completely obtain their classifications.