半群 Oεn的极大幂等元生成子半群
Maximal Idempotent-Generated Subsemigroups of Semigroup Oεn
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摘要: 设Oεn是Xn上的保序且升序变换半群，对橙 n≥3，研究了半群Oεn的极大幂等元生成子半群的结构，证明了半群Oεn的极大子幂等元生成子半群 S有且仅有两类：S＝Oεn＼｛∈｝和 S＝ In－2∪｛∈｝∪ Gm （1≤ m≤ n－1），其中 In－2＝｛α∈Oεn ：｜im（α）｜≤ n－2｝，Gm＝｛α∈Oεn ：｜im（α）｜＝ n－1，mα＝ m｝，∈是集合Xn上的恒等变换。
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关键词:
- 保序、极大子半群、极大幂等元生成子半群
Abstract: Let Oεn be the semigroup of all increasing and order-preserving full transformations on Xn .For arbitrary n such that n≥3 ,the structures of the maximal idempotent-generated subsemigroups of the sem-igroup Oεn were studied .The authors have proved that the semigroup Oεn has exactly two classes of maxi-mal idempotent-generated subsemigroups :S=Oεn\{∈}and S= In-2 ∪{∈}∪ Gm(1≤ m≤ n-1) ,where In-2 ={α∈Oεn :|im(α)| ≤ n-2},Gm={α∈Oεn :|im(α)|= n-1 ,mα= m},∈is the identity on Xn . -
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