J-trivial subsemigroups of finite symmetric inverse semigroups
Yang Hao · Journal of Hangzhou Teachers College · 2003
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.