有限对称逆半群的J-平凡子半群

J-trivial subsemigroups of finite symmetric inverse semigroups

令 In 是有限集 Xn ={1 ,2… ,n}上的对称逆半群 .在此得到 In 的 L-平凡子半群、R-平凡子半群、J-平凡子半群三者等价 ,进而得到 In 的每个极大 J-平凡子半群为 DIn(≤ ) ={φ∈ In:xφ≤ x, x∈ domφ},这里≤是 Xn 上的一个全序 。

Let \$I n\$ be a symmetric inverse semigroup on the finite set \$X n={1,2,...,n}.\$In this paper we obtain that if \$S\$ is a subsemigroup of \$I n\$ then \$S\$ is L\|trivial\$S\$ is R\|trivial\$S\$ is J\|trivial. Further every J\|trivial maximal subsemigroup of \$I n\$ is of the form \$DI n(≤)={φ∈I n: xφ≤x,x∈\%dom\%φ}\$ for some totally ordered set \$(X n,≤)\$. We also discuss the consequences of the above result.