半群Oε_n的极大幂等元生成子半群

Maximal Idempotent-Generated Subsemigroups of Semigroup Oε_n

设Oε_n是X_n上的保序且升序变换半群,对_n≥3,研究了半群Oε_n的极大幂等元生成子半群的结构,证明了半群Oε_n的极大子幂等元生成子半群S有且仅有两类:S=Oε_n\{∈}和S=I_(n-2)∪{∈}∪G_m(1≤m≤n-1),其中I_(n-2)={α∈Oε_n:|im(α)|≤n-2},G_m={α∈Oε_n:|im(α)|=n-1,mα=m},∈是集合X_n上的恒等变换.

Let Oεn be the semigroup of all increasing and order-preserving full transformations on Xn.For arbitrary nsuch that n≥3,the structures of the maximal idempotent-generated subsemigroups of the semigroup Oεnwere studied.The authors have proved that the semigroup Oεnhas exactly two classes of maximal idempotent-generated subsemigroups：S=Oεn／{∈}and S=I（n-2）∪{∈}∪Gm（1≤m≤n-1）,where I（n-2）={α∈Oεn：｜im（α）｜ ≤n-2},Gm={α∈Oεn：｜im（α）｜=n-1,mα=m},∈ is the identity on Xn.