A Note on Quotient Semigroups of Finite Order-decreasing Transformation Semigroups
Let Singn be the singular transformation semigroup on the set Xn={1,2,…,n}with order 1<2<…<n.In this paper,we obtain a kind of congruences ρ of the abundant semigroup S-n={α∈Singn|xα≤x,∀x∈Xn},such that the quotient semigroup S-n/ρ is non-regular and neither left nor right abundant.
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