Let Sn and In be symmetric group and symmetric inverse semigroup on Xn={1,2,...,n}respectively.For 0≤r≤n,put I(n,r)={α ∈In:|im(α)| ≤ r},I(n,r)are the two-sided ideals of symmetric inverse semigroup In.For 0 ≤ r ≤ n-1,we need to consider complete classification of the maximal inverse subsemigroup of a semigroup In,r=I(n,r)U Sn.This paper proved that the maximal sub-semigroup and the maximal inverse subsemigroup of In,rare consistent.
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